{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0001","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-single-preimage；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[0],[0,1],[0,1,2],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"images\":[0,1,2,3],\"target_open\":[]}。請依 [n,m,target_open,preimage,preimage_open] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [], [], 是)","explanation_zh":"第二批擴展核對=(4, 4, [], [], 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-single-preimage","seed":202610193001,"parameters":{"n":4,"m":4,"opens_x":[[],[0],[0,1],[0,1,2],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[0,1,2,3],"target_open":[],"domain":"Fin_topological_map","operation":"continuity-single-preimage","semantic_template":"qf-ext19-continuity-single-preimage/{\"images\":[0,1,2,3],\"m\":4,\"n\":4,\"opens_x\":[[],[0],[0,1],[0,1,2],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"target_open\":[]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0002","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-single-preimage；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[1],[0,1],[0,1,2],[0,1,2,3]],\"opens_y\":[[],[1],[1,2],[0,1,2],[0,1,2,3]],\"images\":[1,0,2,3],\"target_open\":[1]}。請依 [n,m,target_open,preimage,preimage_open] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [1], [0], 否)","explanation_zh":"第二批擴展核對=(4, 4, [1], [0], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-single-preimage","seed":202610193002,"parameters":{"n":4,"m":4,"opens_x":[[],[1],[0,1],[0,1,2],[0,1,2,3]],"opens_y":[[],[1],[1,2],[0,1,2],[0,1,2,3]],"images":[1,0,2,3],"target_open":[1],"domain":"Fin_topological_map","operation":"continuity-single-preimage","semantic_template":"qf-ext19-continuity-single-preimage/{\"images\":[1,0,2,3],\"m\":4,\"n\":4,\"opens_x\":[[],[1],[0,1],[0,1,2],[0,1,2,3]],\"opens_y\":[[],[1],[1,2],[0,1,2],[0,1,2,3]],\"target_open\":[1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0003","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-single-preimage；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[2],[0,2],[0,1,2],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"images\":[2,0,1,3],\"target_open\":[1]}。請依 [n,m,target_open,preimage,preimage_open] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [1], [2], 是)","explanation_zh":"第二批擴展核對=(4, 4, [1], [2], 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-single-preimage","seed":202610193003,"parameters":{"n":4,"m":4,"opens_x":[[],[2],[0,2],[0,1,2],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[2,0,1,3],"target_open":[1],"domain":"Fin_topological_map","operation":"continuity-single-preimage","semantic_template":"qf-ext19-continuity-single-preimage/{\"images\":[2,0,1,3],\"m\":4,\"n\":4,\"opens_x\":[[],[2],[0,2],[0,1,2],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"target_open\":[1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0004","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-single-preimage；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[3],[0,3],[0,1,3],[0,1,2,3]],\"opens_y\":[[],[3],[0,3],[0,2,3],[0,1,2,3]],\"images\":[3,0,1,2],\"target_open\":[0,2,3]}。請依 [n,m,target_open,preimage,preimage_open] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [0, 2, 3], [0, 1, 3], 是)","explanation_zh":"第二批擴展核對=(4, 4, [0, 2, 3], [0, 1, 3], 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-single-preimage","seed":202610193004,"parameters":{"n":4,"m":4,"opens_x":[[],[3],[0,3],[0,1,3],[0,1,2,3]],"opens_y":[[],[3],[0,3],[0,2,3],[0,1,2,3]],"images":[3,0,1,2],"target_open":[0,2,3],"domain":"Fin_topological_map","operation":"continuity-single-preimage","semantic_template":"qf-ext19-continuity-single-preimage/{\"images\":[3,0,1,2],\"m\":4,\"n\":4,\"opens_x\":[[],[3],[0,3],[0,1,3],[0,1,2,3]],\"opens_y\":[[],[3],[0,3],[0,2,3],[0,1,2,3]],\"target_open\":[0,2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0005","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-single-preimage；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[0],[0,2],[0,1,2],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"images\":[0,2,1,3],\"target_open\":[2]}。請依 [n,m,target_open,preimage,preimage_open] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [2], [1], 否)","explanation_zh":"第二批擴展核對=(4, 4, [2], [1], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-single-preimage","seed":202610193005,"parameters":{"n":4,"m":4,"opens_x":[[],[0],[0,2],[0,1,2],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[0,2,1,3],"target_open":[2],"domain":"Fin_topological_map","operation":"continuity-single-preimage","semantic_template":"qf-ext19-continuity-single-preimage/{\"images\":[0,2,1,3],\"m\":4,\"n\":4,\"opens_x\":[[],[0],[0,2],[0,1,2],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"target_open\":[2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0006","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-single-preimage；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[1],[1,2],[0,1,2],[0,1,2,3]],\"opens_y\":[[],[1],[0,1],[0,1,2],[0,1,2,3]],\"images\":[1,2,0,3],\"target_open\":[]}。請依 [n,m,target_open,preimage,preimage_open] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [], [], 是)","explanation_zh":"第二批擴展核對=(4, 4, [], [], 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-single-preimage","seed":202610193006,"parameters":{"n":4,"m":4,"opens_x":[[],[1],[1,2],[0,1,2],[0,1,2,3]],"opens_y":[[],[1],[0,1],[0,1,2],[0,1,2,3]],"images":[1,2,0,3],"target_open":[],"domain":"Fin_topological_map","operation":"continuity-single-preimage","semantic_template":"qf-ext19-continuity-single-preimage/{\"images\":[1,2,0,3],\"m\":4,\"n\":4,\"opens_x\":[[],[1],[1,2],[0,1,2],[0,1,2,3]],\"opens_y\":[[],[1],[0,1],[0,1,2],[0,1,2,3]],\"target_open\":[]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0007","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-single-preimage；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[2],[1,2],[0,1,2],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"images\":[2,1,0,3],\"target_open\":[1,2]}。請依 [n,m,target_open,preimage,preimage_open] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [1, 2], [0, 1], 否)","explanation_zh":"第二批擴展核對=(4, 4, [1, 2], [0, 1], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-single-preimage","seed":202610193007,"parameters":{"n":4,"m":4,"opens_x":[[],[2],[1,2],[0,1,2],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[2,1,0,3],"target_open":[1,2],"domain":"Fin_topological_map","operation":"continuity-single-preimage","semantic_template":"qf-ext19-continuity-single-preimage/{\"images\":[2,1,0,3],\"m\":4,\"n\":4,\"opens_x\":[[],[2],[1,2],[0,1,2],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"target_open\":[1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0008","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-single-preimage；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[3],[1,3],[0,1,3],[0,1,2,3]],\"opens_y\":[[],[3],[2,3],[0,2,3],[0,1,2,3]],\"images\":[3,1,0,2],\"target_open\":[2,3]}。請依 [n,m,target_open,preimage,preimage_open] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [2, 3], [0, 3], 否)","explanation_zh":"第二批擴展核對=(4, 4, [2, 3], [0, 3], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-single-preimage","seed":202610193008,"parameters":{"n":4,"m":4,"opens_x":[[],[3],[1,3],[0,1,3],[0,1,2,3]],"opens_y":[[],[3],[2,3],[0,2,3],[0,1,2,3]],"images":[3,1,0,2],"target_open":[2,3],"domain":"Fin_topological_map","operation":"continuity-single-preimage","semantic_template":"qf-ext19-continuity-single-preimage/{\"images\":[3,1,0,2],\"m\":4,\"n\":4,\"opens_x\":[[],[3],[1,3],[0,1,3],[0,1,2,3]],\"opens_y\":[[],[3],[2,3],[0,2,3],[0,1,2,3]],\"target_open\":[2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0009","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-single-preimage；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[0],[0,3],[0,1,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"images\":[0,3,1,2],\"target_open\":[3]}。請依 [n,m,target_open,preimage,preimage_open] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [3], [1], 否)","explanation_zh":"第二批擴展核對=(4, 4, [3], [1], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-single-preimage","seed":202610193009,"parameters":{"n":4,"m":4,"opens_x":[[],[0],[0,3],[0,1,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[0,3,1,2],"target_open":[3],"domain":"Fin_topological_map","operation":"continuity-single-preimage","semantic_template":"qf-ext19-continuity-single-preimage/{\"images\":[0,3,1,2],\"m\":4,\"n\":4,\"opens_x\":[[],[0],[0,3],[0,1,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"target_open\":[3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0010","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-single-preimage；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[1],[1,3],[0,1,3],[0,1,2,3]],\"opens_y\":[[],[1],[1,3],[1,2,3],[0,1,2,3]],\"images\":[1,3,0,2],\"target_open\":[0,1,2,3]}。請依 [n,m,target_open,preimage,preimage_open] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [0, 1, 2, 3], [0, 1, 2, 3], 是)","explanation_zh":"第二批擴展核對=(4, 4, [0, 1, 2, 3], [0, 1, 2, 3], 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-single-preimage","seed":202610193010,"parameters":{"n":4,"m":4,"opens_x":[[],[1],[1,3],[0,1,3],[0,1,2,3]],"opens_y":[[],[1],[1,3],[1,2,3],[0,1,2,3]],"images":[1,3,0,2],"target_open":[0,1,2,3],"domain":"Fin_topological_map","operation":"continuity-single-preimage","semantic_template":"qf-ext19-continuity-single-preimage/{\"images\":[1,3,0,2],\"m\":4,\"n\":4,\"opens_x\":[[],[1],[1,3],[0,1,3],[0,1,2,3]],\"opens_y\":[[],[1],[1,3],[1,2,3],[0,1,2,3]],\"target_open\":[0,1,2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0011","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-single-preimage；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[2],[2,3],[0,2,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"images\":[2,3,0,1],\"target_open\":[1,3]}。請依 [n,m,target_open,preimage,preimage_open] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [1, 3], [1, 3], 否)","explanation_zh":"第二批擴展核對=(4, 4, [1, 3], [1, 3], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-single-preimage","seed":202610193011,"parameters":{"n":4,"m":4,"opens_x":[[],[2],[2,3],[0,2,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[2,3,0,1],"target_open":[1,3],"domain":"Fin_topological_map","operation":"continuity-single-preimage","semantic_template":"qf-ext19-continuity-single-preimage/{\"images\":[2,3,0,1],\"m\":4,\"n\":4,\"opens_x\":[[],[2],[2,3],[0,2,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"target_open\":[1,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0012","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-single-preimage；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[3],[2,3],[0,2,3],[0,1,2,3]],\"opens_y\":[[],[3],[1,3],[0,1,3],[0,1,2,3]],\"images\":[3,2,0,1],\"target_open\":[3]}。請依 [n,m,target_open,preimage,preimage_open] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [3], [0], 否)","explanation_zh":"第二批擴展核對=(4, 4, [3], [0], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-single-preimage","seed":202610193012,"parameters":{"n":4,"m":4,"opens_x":[[],[3],[2,3],[0,2,3],[0,1,2,3]],"opens_y":[[],[3],[1,3],[0,1,3],[0,1,2,3]],"images":[3,2,0,1],"target_open":[3],"domain":"Fin_topological_map","operation":"continuity-single-preimage","semantic_template":"qf-ext19-continuity-single-preimage/{\"images\":[3,2,0,1],\"m\":4,\"n\":4,\"opens_x\":[[],[3],[2,3],[0,2,3],[0,1,2,3]],\"opens_y\":[[],[3],[1,3],[0,1,3],[0,1,2,3]],\"target_open\":[3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0013","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-single-preimage；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[0],[0,1],[0,1,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"images\":[0,1,3,2],\"target_open\":[2,3]}。請依 [n,m,target_open,preimage,preimage_open] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [2, 3], [2, 3], 否)","explanation_zh":"第二批擴展核對=(4, 4, [2, 3], [2, 3], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-single-preimage","seed":202610193013,"parameters":{"n":4,"m":4,"opens_x":[[],[0],[0,1],[0,1,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[0,1,3,2],"target_open":[2,3],"domain":"Fin_topological_map","operation":"continuity-single-preimage","semantic_template":"qf-ext19-continuity-single-preimage/{\"images\":[0,1,3,2],\"m\":4,\"n\":4,\"opens_x\":[[],[0],[0,1],[0,1,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"target_open\":[2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0014","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-single-preimage；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[1],[0,1],[0,1,3],[0,1,2,3]],\"opens_y\":[[],[1],[1,2],[1,2,3],[0,1,2,3]],\"images\":[1,0,3,2],\"target_open\":[1,2,3]}。請依 [n,m,target_open,preimage,preimage_open] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [1, 2, 3], [0, 2, 3], 否)","explanation_zh":"第二批擴展核對=(4, 4, [1, 2, 3], [0, 2, 3], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-single-preimage","seed":202610193014,"parameters":{"n":4,"m":4,"opens_x":[[],[1],[0,1],[0,1,3],[0,1,2,3]],"opens_y":[[],[1],[1,2],[1,2,3],[0,1,2,3]],"images":[1,0,3,2],"target_open":[1,2,3],"domain":"Fin_topological_map","operation":"continuity-single-preimage","semantic_template":"qf-ext19-continuity-single-preimage/{\"images\":[1,0,3,2],\"m\":4,\"n\":4,\"opens_x\":[[],[1],[0,1],[0,1,3],[0,1,2,3]],\"opens_y\":[[],[1],[1,2],[1,2,3],[0,1,2,3]],\"target_open\":[1,2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0015","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-single-preimage；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[2],[0,2],[0,2,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"images\":[2,0,3,1],\"target_open\":[1,2,3]}。請依 [n,m,target_open,preimage,preimage_open] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [1, 2, 3], [0, 2, 3], 是)","explanation_zh":"第二批擴展核對=(4, 4, [1, 2, 3], [0, 2, 3], 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-single-preimage","seed":202610193015,"parameters":{"n":4,"m":4,"opens_x":[[],[2],[0,2],[0,2,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[2,0,3,1],"target_open":[1,2,3],"domain":"Fin_topological_map","operation":"continuity-single-preimage","semantic_template":"qf-ext19-continuity-single-preimage/{\"images\":[2,0,3,1],\"m\":4,\"n\":4,\"opens_x\":[[],[2],[0,2],[0,2,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"target_open\":[1,2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0016","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-single-preimage；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[3],[0,3],[0,2,3],[0,1,2,3]],\"opens_y\":[[],[3],[0,3],[0,1,3],[0,1,2,3]],\"images\":[3,0,2,1],\"target_open\":[]}。請依 [n,m,target_open,preimage,preimage_open] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [], [], 是)","explanation_zh":"第二批擴展核對=(4, 4, [], [], 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-single-preimage","seed":202610193016,"parameters":{"n":4,"m":4,"opens_x":[[],[3],[0,3],[0,2,3],[0,1,2,3]],"opens_y":[[],[3],[0,3],[0,1,3],[0,1,2,3]],"images":[3,0,2,1],"target_open":[],"domain":"Fin_topological_map","operation":"continuity-single-preimage","semantic_template":"qf-ext19-continuity-single-preimage/{\"images\":[3,0,2,1],\"m\":4,\"n\":4,\"opens_x\":[[],[3],[0,3],[0,2,3],[0,1,2,3]],\"opens_y\":[[],[3],[0,3],[0,1,3],[0,1,2,3]],\"target_open\":[]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0017","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-single-preimage；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[0],[0,2],[0,2,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"images\":[0,2,3,1],\"target_open\":[]}。請依 [n,m,target_open,preimage,preimage_open] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [], [], 是)","explanation_zh":"第二批擴展核對=(4, 4, [], [], 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-single-preimage","seed":202610193017,"parameters":{"n":4,"m":4,"opens_x":[[],[0],[0,2],[0,2,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[0,2,3,1],"target_open":[],"domain":"Fin_topological_map","operation":"continuity-single-preimage","semantic_template":"qf-ext19-continuity-single-preimage/{\"images\":[0,2,3,1],\"m\":4,\"n\":4,\"opens_x\":[[],[0],[0,2],[0,2,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"target_open\":[]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0018","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-single-preimage；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[1],[1,2],[1,2,3],[0,1,2,3]],\"opens_y\":[[],[1],[0,1],[0,1,3],[0,1,2,3]],\"images\":[1,2,3,0],\"target_open\":[0,1]}。請依 [n,m,target_open,preimage,preimage_open] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [0, 1], [0, 3], 否)","explanation_zh":"第二批擴展核對=(4, 4, [0, 1], [0, 3], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-single-preimage","seed":202610193018,"parameters":{"n":4,"m":4,"opens_x":[[],[1],[1,2],[1,2,3],[0,1,2,3]],"opens_y":[[],[1],[0,1],[0,1,3],[0,1,2,3]],"images":[1,2,3,0],"target_open":[0,1],"domain":"Fin_topological_map","operation":"continuity-single-preimage","semantic_template":"qf-ext19-continuity-single-preimage/{\"images\":[1,2,3,0],\"m\":4,\"n\":4,\"opens_x\":[[],[1],[1,2],[1,2,3],[0,1,2,3]],\"opens_y\":[[],[1],[0,1],[0,1,3],[0,1,2,3]],\"target_open\":[0,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0019","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-single-preimage；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[2],[1,2],[1,2,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"images\":[2,1,3,0],\"target_open\":[1]}。請依 [n,m,target_open,preimage,preimage_open] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [1], [1], 否)","explanation_zh":"第二批擴展核對=(4, 4, [1], [1], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-single-preimage","seed":202610193019,"parameters":{"n":4,"m":4,"opens_x":[[],[2],[1,2],[1,2,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[2,1,3,0],"target_open":[1],"domain":"Fin_topological_map","operation":"continuity-single-preimage","semantic_template":"qf-ext19-continuity-single-preimage/{\"images\":[2,1,3,0],\"m\":4,\"n\":4,\"opens_x\":[[],[2],[1,2],[1,2,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"target_open\":[1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0020","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-single-preimage；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[3],[1,3],[1,2,3],[0,1,2,3]],\"opens_y\":[[],[3],[2,3],[1,2,3],[0,1,2,3]],\"images\":[3,1,2,0],\"target_open\":[0,1,2,3]}。請依 [n,m,target_open,preimage,preimage_open] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [0, 1, 2, 3], [0, 1, 2, 3], 是)","explanation_zh":"第二批擴展核對=(4, 4, [0, 1, 2, 3], [0, 1, 2, 3], 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-single-preimage","seed":202610193020,"parameters":{"n":4,"m":4,"opens_x":[[],[3],[1,3],[1,2,3],[0,1,2,3]],"opens_y":[[],[3],[2,3],[1,2,3],[0,1,2,3]],"images":[3,1,2,0],"target_open":[0,1,2,3],"domain":"Fin_topological_map","operation":"continuity-single-preimage","semantic_template":"qf-ext19-continuity-single-preimage/{\"images\":[3,1,2,0],\"m\":4,\"n\":4,\"opens_x\":[[],[3],[1,3],[1,2,3],[0,1,2,3]],\"opens_y\":[[],[3],[2,3],[1,2,3],[0,1,2,3]],\"target_open\":[0,1,2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0021","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-single-preimage；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[0],[0,3],[0,2,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"images\":[0,3,2,1],\"target_open\":[2]}。請依 [n,m,target_open,preimage,preimage_open] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [2], [2], 否)","explanation_zh":"第二批擴展核對=(4, 4, [2], [2], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-single-preimage","seed":202610193021,"parameters":{"n":4,"m":4,"opens_x":[[],[0],[0,3],[0,2,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[0,3,2,1],"target_open":[2],"domain":"Fin_topological_map","operation":"continuity-single-preimage","semantic_template":"qf-ext19-continuity-single-preimage/{\"images\":[0,3,2,1],\"m\":4,\"n\":4,\"opens_x\":[[],[0],[0,3],[0,2,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"target_open\":[2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0022","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-single-preimage；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[1],[1,3],[1,2,3],[0,1,2,3]],\"opens_y\":[[],[1],[1,3],[0,1,3],[0,1,2,3]],\"images\":[1,3,2,0],\"target_open\":[1]}。請依 [n,m,target_open,preimage,preimage_open] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [1], [0], 否)","explanation_zh":"第二批擴展核對=(4, 4, [1], [0], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-single-preimage","seed":202610193022,"parameters":{"n":4,"m":4,"opens_x":[[],[1],[1,3],[1,2,3],[0,1,2,3]],"opens_y":[[],[1],[1,3],[0,1,3],[0,1,2,3]],"images":[1,3,2,0],"target_open":[1],"domain":"Fin_topological_map","operation":"continuity-single-preimage","semantic_template":"qf-ext19-continuity-single-preimage/{\"images\":[1,3,2,0],\"m\":4,\"n\":4,\"opens_x\":[[],[1],[1,3],[1,2,3],[0,1,2,3]],\"opens_y\":[[],[1],[1,3],[0,1,3],[0,1,2,3]],\"target_open\":[1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0023","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-single-preimage；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[2],[2,3],[1,2,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"images\":[2,3,1,0],\"target_open\":[1,2]}。請依 [n,m,target_open,preimage,preimage_open] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [1, 2], [0, 2], 否)","explanation_zh":"第二批擴展核對=(4, 4, [1, 2], [0, 2], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-single-preimage","seed":202610193023,"parameters":{"n":4,"m":4,"opens_x":[[],[2],[2,3],[1,2,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[2,3,1,0],"target_open":[1,2],"domain":"Fin_topological_map","operation":"continuity-single-preimage","semantic_template":"qf-ext19-continuity-single-preimage/{\"images\":[2,3,1,0],\"m\":4,\"n\":4,\"opens_x\":[[],[2],[2,3],[1,2,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"target_open\":[1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0024","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-single-preimage；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[3],[2,3],[1,2,3],[0,1,2,3]],\"opens_y\":[[],[3],[1,3],[1,2,3],[0,1,2,3]],\"images\":[3,2,1,0],\"target_open\":[1,2,3]}。請依 [n,m,target_open,preimage,preimage_open] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [1, 2, 3], [0, 1, 2], 否)","explanation_zh":"第二批擴展核對=(4, 4, [1, 2, 3], [0, 1, 2], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-single-preimage","seed":202610193024,"parameters":{"n":4,"m":4,"opens_x":[[],[3],[2,3],[1,2,3],[0,1,2,3]],"opens_y":[[],[3],[1,3],[1,2,3],[0,1,2,3]],"images":[3,2,1,0],"target_open":[1,2,3],"domain":"Fin_topological_map","operation":"continuity-single-preimage","semantic_template":"qf-ext19-continuity-single-preimage/{\"images\":[3,2,1,0],\"m\":4,\"n\":4,\"opens_x\":[[],[3],[2,3],[1,2,3],[0,1,2,3]],\"opens_y\":[[],[3],[1,3],[1,2,3],[0,1,2,3]],\"target_open\":[1,2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0025","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-single-preimage；資料={\"n\":3,\"m\":3,\"opens_x\":[[],[0],[0,1],[0,1,2]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2]],\"images\":[0,1,2],\"target_open\":[]}。請依 [n,m,target_open,preimage,preimage_open] 欄序回答。","answer":{"kind":"expression","value":"(3, 3, [], [], 是)","explanation_zh":"第二批擴展核對=(3, 3, [], [], 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-single-preimage","seed":202610193025,"parameters":{"n":3,"m":3,"opens_x":[[],[0],[0,1],[0,1,2]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2]],"images":[0,1,2],"target_open":[],"domain":"Fin_topological_map","operation":"continuity-single-preimage","semantic_template":"qf-ext19-continuity-single-preimage/{\"images\":[0,1,2],\"m\":3,\"n\":3,\"opens_x\":[[],[0],[0,1],[0,1,2]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2]],\"target_open\":[]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0026","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-full-audit；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[0],[0,1],[0,1,2],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"images\":[0,1,2,3]}。請依 [images,all_target_open_preimage_rows,continuous] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3], [[[], [], 是], [[0], [0], 是], [[1], [1], 否], [[0, 1], [0, 1], 是], [[2], [2], 否], [[0, 2], [0, 2], 否], [[1, 2], [1, 2], 否], [[0, 1, 2], [0, 1, 2], 是], [[3], [3], 否], [[0, 3], [0, 3], 否], [[1, 3], [1, 3], 否], [[0, 1, 3], [0, 1, 3], 否], [[2, 3], [2, 3], 否], [[0, 2, 3], [0, 2, 3], 否], [[1, 2, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)","explanation_zh":"第二批擴展核對=([0, 1, 2, 3], [[[], [], 是], [[0], [0], 是], [[1], [1], 否], [[0, 1], [0, 1], 是], [[2], [2], 否], [[0, 2], [0, 2], 否], [[1, 2], [1, 2], 否], [[0, 1, 2], [0, 1, 2], 是], [[3], [3], 否], [[0, 3], [0, 3], 否], [[1, 3], [1, 3], 否], [[0, 1, 3], [0, 1, 3], 否], [[2, 3], [2, 3], 否], [[0, 2, 3], [0, 2, 3], 否], [[1, 2, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-full-audit","seed":202610193026,"parameters":{"n":4,"m":4,"opens_x":[[],[0],[0,1],[0,1,2],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[0,1,2,3],"domain":"Fin_topological_map","operation":"continuity-full-audit","semantic_template":"qf-ext19-continuity-full-audit/{\"images\":[0,1,2,3],\"m\":4,\"n\":4,\"opens_x\":[[],[0],[0,1],[0,1,2],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0027","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-full-audit；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[1],[0,1],[0,1,2],[0,1,2,3]],\"opens_y\":[[],[1],[1,2],[0,1,2],[0,1,2,3]],\"images\":[1,0,2,3]}。請依 [images,all_target_open_preimage_rows,continuous] 欄序回答。","answer":{"kind":"expression","value":"([1, 0, 2, 3], [[[], [], 是], [[1], [0], 否], [[1, 2], [0, 2], 否], [[0, 1, 2], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)","explanation_zh":"第二批擴展核對=([1, 0, 2, 3], [[[], [], 是], [[1], [0], 否], [[1, 2], [0, 2], 否], [[0, 1, 2], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-full-audit","seed":202610193027,"parameters":{"n":4,"m":4,"opens_x":[[],[1],[0,1],[0,1,2],[0,1,2,3]],"opens_y":[[],[1],[1,2],[0,1,2],[0,1,2,3]],"images":[1,0,2,3],"domain":"Fin_topological_map","operation":"continuity-full-audit","semantic_template":"qf-ext19-continuity-full-audit/{\"images\":[1,0,2,3],\"m\":4,\"n\":4,\"opens_x\":[[],[1],[0,1],[0,1,2],[0,1,2,3]],\"opens_y\":[[],[1],[1,2],[0,1,2],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0028","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-full-audit；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[2],[0,2],[0,1,2],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"images\":[2,0,1,3]}。請依 [images,all_target_open_preimage_rows,continuous] 欄序回答。","answer":{"kind":"expression","value":"([2, 0, 1, 3], [[[], [], 是], [[0], [1], 否], [[1], [2], 是], [[0, 1], [1, 2], 否], [[2], [0], 否], [[0, 2], [0, 1], 否], [[1, 2], [0, 2], 是], [[0, 1, 2], [0, 1, 2], 是], [[3], [3], 否], [[0, 3], [1, 3], 否], [[1, 3], [2, 3], 否], [[0, 1, 3], [1, 2, 3], 否], [[2, 3], [0, 3], 否], [[0, 2, 3], [0, 1, 3], 否], [[1, 2, 3], [0, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)","explanation_zh":"第二批擴展核對=([2, 0, 1, 3], [[[], [], 是], [[0], [1], 否], [[1], [2], 是], [[0, 1], [1, 2], 否], [[2], [0], 否], [[0, 2], [0, 1], 否], [[1, 2], [0, 2], 是], [[0, 1, 2], [0, 1, 2], 是], [[3], [3], 否], [[0, 3], [1, 3], 否], [[1, 3], [2, 3], 否], [[0, 1, 3], [1, 2, 3], 否], [[2, 3], [0, 3], 否], [[0, 2, 3], [0, 1, 3], 否], [[1, 2, 3], [0, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-full-audit","seed":202610193028,"parameters":{"n":4,"m":4,"opens_x":[[],[2],[0,2],[0,1,2],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[2,0,1,3],"domain":"Fin_topological_map","operation":"continuity-full-audit","semantic_template":"qf-ext19-continuity-full-audit/{\"images\":[2,0,1,3],\"m\":4,\"n\":4,\"opens_x\":[[],[2],[0,2],[0,1,2],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0029","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-full-audit；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[3],[0,3],[0,1,3],[0,1,2,3]],\"opens_y\":[[],[3],[0,3],[0,2,3],[0,1,2,3]],\"images\":[3,0,1,2]}。請依 [images,all_target_open_preimage_rows,continuous] 欄序回答。","answer":{"kind":"expression","value":"([3, 0, 1, 2], [[[], [], 是], [[3], [0], 否], [[0, 3], [0, 1], 否], [[0, 2, 3], [0, 1, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)","explanation_zh":"第二批擴展核對=([3, 0, 1, 2], [[[], [], 是], [[3], [0], 否], [[0, 3], [0, 1], 否], [[0, 2, 3], [0, 1, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-full-audit","seed":202610193029,"parameters":{"n":4,"m":4,"opens_x":[[],[3],[0,3],[0,1,3],[0,1,2,3]],"opens_y":[[],[3],[0,3],[0,2,3],[0,1,2,3]],"images":[3,0,1,2],"domain":"Fin_topological_map","operation":"continuity-full-audit","semantic_template":"qf-ext19-continuity-full-audit/{\"images\":[3,0,1,2],\"m\":4,\"n\":4,\"opens_x\":[[],[3],[0,3],[0,1,3],[0,1,2,3]],\"opens_y\":[[],[3],[0,3],[0,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0030","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-full-audit；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[0],[0,2],[0,1,2],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"images\":[0,2,1,3]}。請依 [images,all_target_open_preimage_rows,continuous] 欄序回答。","answer":{"kind":"expression","value":"([0, 2, 1, 3], [[[], [], 是], [[0], [0], 是], [[1], [2], 否], [[0, 1], [0, 2], 是], [[2], [1], 否], [[0, 2], [0, 1], 否], [[1, 2], [1, 2], 否], [[0, 1, 2], [0, 1, 2], 是], [[3], [3], 否], [[0, 3], [0, 3], 否], [[1, 3], [2, 3], 否], [[0, 1, 3], [0, 2, 3], 否], [[2, 3], [1, 3], 否], [[0, 2, 3], [0, 1, 3], 否], [[1, 2, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)","explanation_zh":"第二批擴展核對=([0, 2, 1, 3], [[[], [], 是], [[0], [0], 是], [[1], [2], 否], [[0, 1], [0, 2], 是], [[2], [1], 否], [[0, 2], [0, 1], 否], [[1, 2], [1, 2], 否], [[0, 1, 2], [0, 1, 2], 是], [[3], [3], 否], [[0, 3], [0, 3], 否], [[1, 3], [2, 3], 否], [[0, 1, 3], [0, 2, 3], 否], [[2, 3], [1, 3], 否], [[0, 2, 3], [0, 1, 3], 否], [[1, 2, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-full-audit","seed":202610193030,"parameters":{"n":4,"m":4,"opens_x":[[],[0],[0,2],[0,1,2],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[0,2,1,3],"domain":"Fin_topological_map","operation":"continuity-full-audit","semantic_template":"qf-ext19-continuity-full-audit/{\"images\":[0,2,1,3],\"m\":4,\"n\":4,\"opens_x\":[[],[0],[0,2],[0,1,2],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0031","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-full-audit；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[1],[1,2],[0,1,2],[0,1,2,3]],\"opens_y\":[[],[1],[0,1],[0,1,2],[0,1,2,3]],\"images\":[1,2,0,3]}。請依 [images,all_target_open_preimage_rows,continuous] 欄序回答。","answer":{"kind":"expression","value":"([1, 2, 0, 3], [[[], [], 是], [[1], [0], 否], [[0, 1], [0, 2], 否], [[0, 1, 2], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)","explanation_zh":"第二批擴展核對=([1, 2, 0, 3], [[[], [], 是], [[1], [0], 否], [[0, 1], [0, 2], 否], [[0, 1, 2], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-full-audit","seed":202610193031,"parameters":{"n":4,"m":4,"opens_x":[[],[1],[1,2],[0,1,2],[0,1,2,3]],"opens_y":[[],[1],[0,1],[0,1,2],[0,1,2,3]],"images":[1,2,0,3],"domain":"Fin_topological_map","operation":"continuity-full-audit","semantic_template":"qf-ext19-continuity-full-audit/{\"images\":[1,2,0,3],\"m\":4,\"n\":4,\"opens_x\":[[],[1],[1,2],[0,1,2],[0,1,2,3]],\"opens_y\":[[],[1],[0,1],[0,1,2],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0032","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-full-audit；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[2],[1,2],[0,1,2],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"images\":[2,1,0,3]}。請依 [images,all_target_open_preimage_rows,continuous] 欄序回答。","answer":{"kind":"expression","value":"([2, 1, 0, 3], [[[], [], 是], [[0], [2], 是], [[1], [1], 否], [[0, 1], [1, 2], 是], [[2], [0], 否], [[0, 2], [0, 2], 否], [[1, 2], [0, 1], 否], [[0, 1, 2], [0, 1, 2], 是], [[3], [3], 否], [[0, 3], [2, 3], 否], [[1, 3], [1, 3], 否], [[0, 1, 3], [1, 2, 3], 否], [[2, 3], [0, 3], 否], [[0, 2, 3], [0, 2, 3], 否], [[1, 2, 3], [0, 1, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)","explanation_zh":"第二批擴展核對=([2, 1, 0, 3], [[[], [], 是], [[0], [2], 是], [[1], [1], 否], [[0, 1], [1, 2], 是], [[2], [0], 否], [[0, 2], [0, 2], 否], [[1, 2], [0, 1], 否], [[0, 1, 2], [0, 1, 2], 是], [[3], [3], 否], [[0, 3], [2, 3], 否], [[1, 3], [1, 3], 否], [[0, 1, 3], [1, 2, 3], 否], [[2, 3], [0, 3], 否], [[0, 2, 3], [0, 2, 3], 否], [[1, 2, 3], [0, 1, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-full-audit","seed":202610193032,"parameters":{"n":4,"m":4,"opens_x":[[],[2],[1,2],[0,1,2],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[2,1,0,3],"domain":"Fin_topological_map","operation":"continuity-full-audit","semantic_template":"qf-ext19-continuity-full-audit/{\"images\":[2,1,0,3],\"m\":4,\"n\":4,\"opens_x\":[[],[2],[1,2],[0,1,2],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0033","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-full-audit；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[3],[1,3],[0,1,3],[0,1,2,3]],\"opens_y\":[[],[3],[2,3],[0,2,3],[0,1,2,3]],\"images\":[3,1,0,2]}。請依 [images,all_target_open_preimage_rows,continuous] 欄序回答。","answer":{"kind":"expression","value":"([3, 1, 0, 2], [[[], [], 是], [[3], [0], 否], [[2, 3], [0, 3], 否], [[0, 2, 3], [0, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)","explanation_zh":"第二批擴展核對=([3, 1, 0, 2], [[[], [], 是], [[3], [0], 否], [[2, 3], [0, 3], 否], [[0, 2, 3], [0, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-full-audit","seed":202610193033,"parameters":{"n":4,"m":4,"opens_x":[[],[3],[1,3],[0,1,3],[0,1,2,3]],"opens_y":[[],[3],[2,3],[0,2,3],[0,1,2,3]],"images":[3,1,0,2],"domain":"Fin_topological_map","operation":"continuity-full-audit","semantic_template":"qf-ext19-continuity-full-audit/{\"images\":[3,1,0,2],\"m\":4,\"n\":4,\"opens_x\":[[],[3],[1,3],[0,1,3],[0,1,2,3]],\"opens_y\":[[],[3],[2,3],[0,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0034","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-full-audit；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[0],[0,3],[0,1,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"images\":[0,3,1,2]}。請依 [images,all_target_open_preimage_rows,continuous] 欄序回答。","answer":{"kind":"expression","value":"([0, 3, 1, 2], [[[], [], 是], [[0], [0], 是], [[1], [2], 否], [[0, 1], [0, 2], 否], [[2], [3], 否], [[0, 2], [0, 3], 是], [[1, 2], [2, 3], 否], [[0, 1, 2], [0, 2, 3], 否], [[3], [1], 否], [[0, 3], [0, 1], 否], [[1, 3], [1, 2], 否], [[0, 1, 3], [0, 1, 2], 否], [[2, 3], [1, 3], 否], [[0, 2, 3], [0, 1, 3], 是], [[1, 2, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)","explanation_zh":"第二批擴展核對=([0, 3, 1, 2], [[[], [], 是], [[0], [0], 是], [[1], [2], 否], [[0, 1], [0, 2], 否], [[2], [3], 否], [[0, 2], [0, 3], 是], [[1, 2], [2, 3], 否], [[0, 1, 2], [0, 2, 3], 否], [[3], [1], 否], [[0, 3], [0, 1], 否], [[1, 3], [1, 2], 否], [[0, 1, 3], [0, 1, 2], 否], [[2, 3], [1, 3], 否], [[0, 2, 3], [0, 1, 3], 是], [[1, 2, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-full-audit","seed":202610193034,"parameters":{"n":4,"m":4,"opens_x":[[],[0],[0,3],[0,1,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[0,3,1,2],"domain":"Fin_topological_map","operation":"continuity-full-audit","semantic_template":"qf-ext19-continuity-full-audit/{\"images\":[0,3,1,2],\"m\":4,\"n\":4,\"opens_x\":[[],[0],[0,3],[0,1,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0035","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-full-audit；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[1],[1,3],[0,1,3],[0,1,2,3]],\"opens_y\":[[],[1],[1,3],[1,2,3],[0,1,2,3]],\"images\":[1,3,0,2]}。請依 [images,all_target_open_preimage_rows,continuous] 欄序回答。","answer":{"kind":"expression","value":"([1, 3, 0, 2], [[[], [], 是], [[1], [0], 否], [[1, 3], [0, 1], 否], [[1, 2, 3], [0, 1, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)","explanation_zh":"第二批擴展核對=([1, 3, 0, 2], [[[], [], 是], [[1], [0], 否], [[1, 3], [0, 1], 否], [[1, 2, 3], [0, 1, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-full-audit","seed":202610193035,"parameters":{"n":4,"m":4,"opens_x":[[],[1],[1,3],[0,1,3],[0,1,2,3]],"opens_y":[[],[1],[1,3],[1,2,3],[0,1,2,3]],"images":[1,3,0,2],"domain":"Fin_topological_map","operation":"continuity-full-audit","semantic_template":"qf-ext19-continuity-full-audit/{\"images\":[1,3,0,2],\"m\":4,\"n\":4,\"opens_x\":[[],[1],[1,3],[0,1,3],[0,1,2,3]],\"opens_y\":[[],[1],[1,3],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0036","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-full-audit；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[2],[2,3],[0,2,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"images\":[2,3,0,1]}。請依 [images,all_target_open_preimage_rows,continuous] 欄序回答。","answer":{"kind":"expression","value":"([2, 3, 0, 1], [[[], [], 是], [[0], [2], 是], [[1], [3], 否], [[0, 1], [2, 3], 是], [[2], [0], 否], [[0, 2], [0, 2], 否], [[1, 2], [0, 3], 否], [[0, 1, 2], [0, 2, 3], 是], [[3], [1], 否], [[0, 3], [1, 2], 否], [[1, 3], [1, 3], 否], [[0, 1, 3], [1, 2, 3], 否], [[2, 3], [0, 1], 否], [[0, 2, 3], [0, 1, 2], 否], [[1, 2, 3], [0, 1, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)","explanation_zh":"第二批擴展核對=([2, 3, 0, 1], [[[], [], 是], [[0], [2], 是], [[1], [3], 否], [[0, 1], [2, 3], 是], [[2], [0], 否], [[0, 2], [0, 2], 否], [[1, 2], [0, 3], 否], [[0, 1, 2], [0, 2, 3], 是], [[3], [1], 否], [[0, 3], [1, 2], 否], [[1, 3], [1, 3], 否], [[0, 1, 3], [1, 2, 3], 否], [[2, 3], [0, 1], 否], [[0, 2, 3], [0, 1, 2], 否], [[1, 2, 3], [0, 1, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-full-audit","seed":202610193036,"parameters":{"n":4,"m":4,"opens_x":[[],[2],[2,3],[0,2,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[2,3,0,1],"domain":"Fin_topological_map","operation":"continuity-full-audit","semantic_template":"qf-ext19-continuity-full-audit/{\"images\":[2,3,0,1],\"m\":4,\"n\":4,\"opens_x\":[[],[2],[2,3],[0,2,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0037","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-full-audit；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[3],[2,3],[0,2,3],[0,1,2,3]],\"opens_y\":[[],[3],[1,3],[0,1,3],[0,1,2,3]],\"images\":[3,2,0,1]}。請依 [images,all_target_open_preimage_rows,continuous] 欄序回答。","answer":{"kind":"expression","value":"([3, 2, 0, 1], [[[], [], 是], [[3], [0], 否], [[1, 3], [0, 3], 否], [[0, 1, 3], [0, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)","explanation_zh":"第二批擴展核對=([3, 2, 0, 1], [[[], [], 是], [[3], [0], 否], [[1, 3], [0, 3], 否], [[0, 1, 3], [0, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-full-audit","seed":202610193037,"parameters":{"n":4,"m":4,"opens_x":[[],[3],[2,3],[0,2,3],[0,1,2,3]],"opens_y":[[],[3],[1,3],[0,1,3],[0,1,2,3]],"images":[3,2,0,1],"domain":"Fin_topological_map","operation":"continuity-full-audit","semantic_template":"qf-ext19-continuity-full-audit/{\"images\":[3,2,0,1],\"m\":4,\"n\":4,\"opens_x\":[[],[3],[2,3],[0,2,3],[0,1,2,3]],\"opens_y\":[[],[3],[1,3],[0,1,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0038","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-full-audit；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[0],[0,1],[0,1,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"images\":[0,1,3,2]}。請依 [images,all_target_open_preimage_rows,continuous] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 3, 2], [[[], [], 是], [[0], [0], 是], [[1], [1], 否], [[0, 1], [0, 1], 是], [[2], [3], 否], [[0, 2], [0, 3], 否], [[1, 2], [1, 3], 否], [[0, 1, 2], [0, 1, 3], 是], [[3], [2], 否], [[0, 3], [0, 2], 否], [[1, 3], [1, 2], 否], [[0, 1, 3], [0, 1, 2], 否], [[2, 3], [2, 3], 否], [[0, 2, 3], [0, 2, 3], 否], [[1, 2, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)","explanation_zh":"第二批擴展核對=([0, 1, 3, 2], [[[], [], 是], [[0], [0], 是], [[1], [1], 否], [[0, 1], [0, 1], 是], [[2], [3], 否], [[0, 2], [0, 3], 否], [[1, 2], [1, 3], 否], [[0, 1, 2], [0, 1, 3], 是], [[3], [2], 否], [[0, 3], [0, 2], 否], [[1, 3], [1, 2], 否], [[0, 1, 3], [0, 1, 2], 否], [[2, 3], [2, 3], 否], [[0, 2, 3], [0, 2, 3], 否], [[1, 2, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-full-audit","seed":202610193038,"parameters":{"n":4,"m":4,"opens_x":[[],[0],[0,1],[0,1,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[0,1,3,2],"domain":"Fin_topological_map","operation":"continuity-full-audit","semantic_template":"qf-ext19-continuity-full-audit/{\"images\":[0,1,3,2],\"m\":4,\"n\":4,\"opens_x\":[[],[0],[0,1],[0,1,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0039","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-full-audit；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[1],[0,1],[0,1,3],[0,1,2,3]],\"opens_y\":[[],[1],[1,2],[1,2,3],[0,1,2,3]],\"images\":[1,0,3,2]}。請依 [images,all_target_open_preimage_rows,continuous] 欄序回答。","answer":{"kind":"expression","value":"([1, 0, 3, 2], [[[], [], 是], [[1], [0], 否], [[1, 2], [0, 3], 否], [[1, 2, 3], [0, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)","explanation_zh":"第二批擴展核對=([1, 0, 3, 2], [[[], [], 是], [[1], [0], 否], [[1, 2], [0, 3], 否], [[1, 2, 3], [0, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-full-audit","seed":202610193039,"parameters":{"n":4,"m":4,"opens_x":[[],[1],[0,1],[0,1,3],[0,1,2,3]],"opens_y":[[],[1],[1,2],[1,2,3],[0,1,2,3]],"images":[1,0,3,2],"domain":"Fin_topological_map","operation":"continuity-full-audit","semantic_template":"qf-ext19-continuity-full-audit/{\"images\":[1,0,3,2],\"m\":4,\"n\":4,\"opens_x\":[[],[1],[0,1],[0,1,3],[0,1,2,3]],\"opens_y\":[[],[1],[1,2],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0040","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-full-audit；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[2],[0,2],[0,2,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"images\":[2,0,3,1]}。請依 [images,all_target_open_preimage_rows,continuous] 欄序回答。","answer":{"kind":"expression","value":"([2, 0, 3, 1], [[[], [], 是], [[0], [1], 否], [[1], [3], 否], [[0, 1], [1, 3], 否], [[2], [0], 否], [[0, 2], [0, 1], 否], [[1, 2], [0, 3], 否], [[0, 1, 2], [0, 1, 3], 否], [[3], [2], 是], [[0, 3], [1, 2], 否], [[1, 3], [2, 3], 否], [[0, 1, 3], [1, 2, 3], 否], [[2, 3], [0, 2], 是], [[0, 2, 3], [0, 1, 2], 否], [[1, 2, 3], [0, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)","explanation_zh":"第二批擴展核對=([2, 0, 3, 1], [[[], [], 是], [[0], [1], 否], [[1], [3], 否], [[0, 1], [1, 3], 否], [[2], [0], 否], [[0, 2], [0, 1], 否], [[1, 2], [0, 3], 否], [[0, 1, 2], [0, 1, 3], 否], [[3], [2], 是], [[0, 3], [1, 2], 否], [[1, 3], [2, 3], 否], [[0, 1, 3], [1, 2, 3], 否], [[2, 3], [0, 2], 是], [[0, 2, 3], [0, 1, 2], 否], [[1, 2, 3], [0, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-full-audit","seed":202610193040,"parameters":{"n":4,"m":4,"opens_x":[[],[2],[0,2],[0,2,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[2,0,3,1],"domain":"Fin_topological_map","operation":"continuity-full-audit","semantic_template":"qf-ext19-continuity-full-audit/{\"images\":[2,0,3,1],\"m\":4,\"n\":4,\"opens_x\":[[],[2],[0,2],[0,2,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0041","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-full-audit；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[3],[0,3],[0,2,3],[0,1,2,3]],\"opens_y\":[[],[3],[0,3],[0,1,3],[0,1,2,3]],\"images\":[3,0,2,1]}。請依 [images,all_target_open_preimage_rows,continuous] 欄序回答。","answer":{"kind":"expression","value":"([3, 0, 2, 1], [[[], [], 是], [[3], [0], 否], [[0, 3], [0, 1], 否], [[0, 1, 3], [0, 1, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)","explanation_zh":"第二批擴展核對=([3, 0, 2, 1], [[[], [], 是], [[3], [0], 否], [[0, 3], [0, 1], 否], [[0, 1, 3], [0, 1, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-full-audit","seed":202610193041,"parameters":{"n":4,"m":4,"opens_x":[[],[3],[0,3],[0,2,3],[0,1,2,3]],"opens_y":[[],[3],[0,3],[0,1,3],[0,1,2,3]],"images":[3,0,2,1],"domain":"Fin_topological_map","operation":"continuity-full-audit","semantic_template":"qf-ext19-continuity-full-audit/{\"images\":[3,0,2,1],\"m\":4,\"n\":4,\"opens_x\":[[],[3],[0,3],[0,2,3],[0,1,2,3]],\"opens_y\":[[],[3],[0,3],[0,1,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0042","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-full-audit；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[0],[0,2],[0,2,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"images\":[0,2,3,1]}。請依 [images,all_target_open_preimage_rows,continuous] 欄序回答。","answer":{"kind":"expression","value":"([0, 2, 3, 1], [[[], [], 是], [[0], [0], 是], [[1], [3], 否], [[0, 1], [0, 3], 否], [[2], [1], 否], [[0, 2], [0, 1], 否], [[1, 2], [1, 3], 否], [[0, 1, 2], [0, 1, 3], 否], [[3], [2], 否], [[0, 3], [0, 2], 是], [[1, 3], [2, 3], 否], [[0, 1, 3], [0, 2, 3], 是], [[2, 3], [1, 2], 否], [[0, 2, 3], [0, 1, 2], 否], [[1, 2, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)","explanation_zh":"第二批擴展核對=([0, 2, 3, 1], [[[], [], 是], [[0], [0], 是], [[1], [3], 否], [[0, 1], [0, 3], 否], [[2], [1], 否], [[0, 2], [0, 1], 否], [[1, 2], [1, 3], 否], [[0, 1, 2], [0, 1, 3], 否], [[3], [2], 否], [[0, 3], [0, 2], 是], [[1, 3], [2, 3], 否], [[0, 1, 3], [0, 2, 3], 是], [[2, 3], [1, 2], 否], [[0, 2, 3], [0, 1, 2], 否], [[1, 2, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-full-audit","seed":202610193042,"parameters":{"n":4,"m":4,"opens_x":[[],[0],[0,2],[0,2,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[0,2,3,1],"domain":"Fin_topological_map","operation":"continuity-full-audit","semantic_template":"qf-ext19-continuity-full-audit/{\"images\":[0,2,3,1],\"m\":4,\"n\":4,\"opens_x\":[[],[0],[0,2],[0,2,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0043","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-full-audit；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[1],[1,2],[1,2,3],[0,1,2,3]],\"opens_y\":[[],[1],[0,1],[0,1,3],[0,1,2,3]],\"images\":[1,2,3,0]}。請依 [images,all_target_open_preimage_rows,continuous] 欄序回答。","answer":{"kind":"expression","value":"([1, 2, 3, 0], [[[], [], 是], [[1], [0], 否], [[0, 1], [0, 3], 否], [[0, 1, 3], [0, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)","explanation_zh":"第二批擴展核對=([1, 2, 3, 0], [[[], [], 是], [[1], [0], 否], [[0, 1], [0, 3], 否], [[0, 1, 3], [0, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-full-audit","seed":202610193043,"parameters":{"n":4,"m":4,"opens_x":[[],[1],[1,2],[1,2,3],[0,1,2,3]],"opens_y":[[],[1],[0,1],[0,1,3],[0,1,2,3]],"images":[1,2,3,0],"domain":"Fin_topological_map","operation":"continuity-full-audit","semantic_template":"qf-ext19-continuity-full-audit/{\"images\":[1,2,3,0],\"m\":4,\"n\":4,\"opens_x\":[[],[1],[1,2],[1,2,3],[0,1,2,3]],\"opens_y\":[[],[1],[0,1],[0,1,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0044","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-full-audit；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[2],[1,2],[1,2,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"images\":[2,1,3,0]}。請依 [images,all_target_open_preimage_rows,continuous] 欄序回答。","answer":{"kind":"expression","value":"([2, 1, 3, 0], [[[], [], 是], [[0], [3], 否], [[1], [1], 否], [[0, 1], [1, 3], 否], [[2], [0], 否], [[0, 2], [0, 3], 否], [[1, 2], [0, 1], 否], [[0, 1, 2], [0, 1, 3], 否], [[3], [2], 是], [[0, 3], [2, 3], 否], [[1, 3], [1, 2], 是], [[0, 1, 3], [1, 2, 3], 是], [[2, 3], [0, 2], 否], [[0, 2, 3], [0, 2, 3], 否], [[1, 2, 3], [0, 1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)","explanation_zh":"第二批擴展核對=([2, 1, 3, 0], [[[], [], 是], [[0], [3], 否], [[1], [1], 否], [[0, 1], [1, 3], 否], [[2], [0], 否], [[0, 2], [0, 3], 否], [[1, 2], [0, 1], 否], [[0, 1, 2], [0, 1, 3], 否], [[3], [2], 是], [[0, 3], [2, 3], 否], [[1, 3], [1, 2], 是], [[0, 1, 3], [1, 2, 3], 是], [[2, 3], [0, 2], 否], [[0, 2, 3], [0, 2, 3], 否], [[1, 2, 3], [0, 1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-full-audit","seed":202610193044,"parameters":{"n":4,"m":4,"opens_x":[[],[2],[1,2],[1,2,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[2,1,3,0],"domain":"Fin_topological_map","operation":"continuity-full-audit","semantic_template":"qf-ext19-continuity-full-audit/{\"images\":[2,1,3,0],\"m\":4,\"n\":4,\"opens_x\":[[],[2],[1,2],[1,2,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0045","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-full-audit；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[3],[1,3],[1,2,3],[0,1,2,3]],\"opens_y\":[[],[3],[2,3],[1,2,3],[0,1,2,3]],\"images\":[3,1,2,0]}。請依 [images,all_target_open_preimage_rows,continuous] 欄序回答。","answer":{"kind":"expression","value":"([3, 1, 2, 0], [[[], [], 是], [[3], [0], 否], [[2, 3], [0, 2], 否], [[1, 2, 3], [0, 1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)","explanation_zh":"第二批擴展核對=([3, 1, 2, 0], [[[], [], 是], [[3], [0], 否], [[2, 3], [0, 2], 否], [[1, 2, 3], [0, 1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-full-audit","seed":202610193045,"parameters":{"n":4,"m":4,"opens_x":[[],[3],[1,3],[1,2,3],[0,1,2,3]],"opens_y":[[],[3],[2,3],[1,2,3],[0,1,2,3]],"images":[3,1,2,0],"domain":"Fin_topological_map","operation":"continuity-full-audit","semantic_template":"qf-ext19-continuity-full-audit/{\"images\":[3,1,2,0],\"m\":4,\"n\":4,\"opens_x\":[[],[3],[1,3],[1,2,3],[0,1,2,3]],\"opens_y\":[[],[3],[2,3],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0046","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-full-audit；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[0],[0,3],[0,2,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"images\":[0,3,2,1]}。請依 [images,all_target_open_preimage_rows,continuous] 欄序回答。","answer":{"kind":"expression","value":"([0, 3, 2, 1], [[[], [], 是], [[0], [0], 是], [[1], [3], 否], [[0, 1], [0, 3], 是], [[2], [2], 否], [[0, 2], [0, 2], 否], [[1, 2], [2, 3], 否], [[0, 1, 2], [0, 2, 3], 是], [[3], [1], 否], [[0, 3], [0, 1], 否], [[1, 3], [1, 3], 否], [[0, 1, 3], [0, 1, 3], 否], [[2, 3], [1, 2], 否], [[0, 2, 3], [0, 1, 2], 否], [[1, 2, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)","explanation_zh":"第二批擴展核對=([0, 3, 2, 1], [[[], [], 是], [[0], [0], 是], [[1], [3], 否], [[0, 1], [0, 3], 是], [[2], [2], 否], [[0, 2], [0, 2], 否], [[1, 2], [2, 3], 否], [[0, 1, 2], [0, 2, 3], 是], [[3], [1], 否], [[0, 3], [0, 1], 否], [[1, 3], [1, 3], 否], [[0, 1, 3], [0, 1, 3], 否], [[2, 3], [1, 2], 否], [[0, 2, 3], [0, 1, 2], 否], [[1, 2, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-full-audit","seed":202610193046,"parameters":{"n":4,"m":4,"opens_x":[[],[0],[0,3],[0,2,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[0,3,2,1],"domain":"Fin_topological_map","operation":"continuity-full-audit","semantic_template":"qf-ext19-continuity-full-audit/{\"images\":[0,3,2,1],\"m\":4,\"n\":4,\"opens_x\":[[],[0],[0,3],[0,2,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0047","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-full-audit；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[1],[1,3],[1,2,3],[0,1,2,3]],\"opens_y\":[[],[1],[1,3],[0,1,3],[0,1,2,3]],\"images\":[1,3,2,0]}。請依 [images,all_target_open_preimage_rows,continuous] 欄序回答。","answer":{"kind":"expression","value":"([1, 3, 2, 0], [[[], [], 是], [[1], [0], 否], [[1, 3], [0, 1], 否], [[0, 1, 3], [0, 1, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)","explanation_zh":"第二批擴展核對=([1, 3, 2, 0], [[[], [], 是], [[1], [0], 否], [[1, 3], [0, 1], 否], [[0, 1, 3], [0, 1, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-full-audit","seed":202610193047,"parameters":{"n":4,"m":4,"opens_x":[[],[1],[1,3],[1,2,3],[0,1,2,3]],"opens_y":[[],[1],[1,3],[0,1,3],[0,1,2,3]],"images":[1,3,2,0],"domain":"Fin_topological_map","operation":"continuity-full-audit","semantic_template":"qf-ext19-continuity-full-audit/{\"images\":[1,3,2,0],\"m\":4,\"n\":4,\"opens_x\":[[],[1],[1,3],[1,2,3],[0,1,2,3]],\"opens_y\":[[],[1],[1,3],[0,1,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0048","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-full-audit；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[2],[2,3],[1,2,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"images\":[2,3,1,0]}。請依 [images,all_target_open_preimage_rows,continuous] 欄序回答。","answer":{"kind":"expression","value":"([2, 3, 1, 0], [[[], [], 是], [[0], [3], 否], [[1], [2], 是], [[0, 1], [2, 3], 是], [[2], [0], 否], [[0, 2], [0, 3], 否], [[1, 2], [0, 2], 否], [[0, 1, 2], [0, 2, 3], 否], [[3], [1], 否], [[0, 3], [1, 3], 否], [[1, 3], [1, 2], 否], [[0, 1, 3], [1, 2, 3], 是], [[2, 3], [0, 1], 否], [[0, 2, 3], [0, 1, 3], 否], [[1, 2, 3], [0, 1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)","explanation_zh":"第二批擴展核對=([2, 3, 1, 0], [[[], [], 是], [[0], [3], 否], [[1], [2], 是], [[0, 1], [2, 3], 是], [[2], [0], 否], [[0, 2], [0, 3], 否], [[1, 2], [0, 2], 否], [[0, 1, 2], [0, 2, 3], 否], [[3], [1], 否], [[0, 3], [1, 3], 否], [[1, 3], [1, 2], 否], [[0, 1, 3], [1, 2, 3], 是], [[2, 3], [0, 1], 否], [[0, 2, 3], [0, 1, 3], 否], [[1, 2, 3], [0, 1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-full-audit","seed":202610193048,"parameters":{"n":4,"m":4,"opens_x":[[],[2],[2,3],[1,2,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[2,3,1,0],"domain":"Fin_topological_map","operation":"continuity-full-audit","semantic_template":"qf-ext19-continuity-full-audit/{\"images\":[2,3,1,0],\"m\":4,\"n\":4,\"opens_x\":[[],[2],[2,3],[1,2,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0049","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-full-audit；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[3],[2,3],[1,2,3],[0,1,2,3]],\"opens_y\":[[],[3],[1,3],[1,2,3],[0,1,2,3]],\"images\":[3,2,1,0]}。請依 [images,all_target_open_preimage_rows,continuous] 欄序回答。","answer":{"kind":"expression","value":"([3, 2, 1, 0], [[[], [], 是], [[3], [0], 否], [[1, 3], [0, 2], 否], [[1, 2, 3], [0, 1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)","explanation_zh":"第二批擴展核對=([3, 2, 1, 0], [[[], [], 是], [[3], [0], 否], [[1, 3], [0, 2], 否], [[1, 2, 3], [0, 1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-full-audit","seed":202610193049,"parameters":{"n":4,"m":4,"opens_x":[[],[3],[2,3],[1,2,3],[0,1,2,3]],"opens_y":[[],[3],[1,3],[1,2,3],[0,1,2,3]],"images":[3,2,1,0],"domain":"Fin_topological_map","operation":"continuity-full-audit","semantic_template":"qf-ext19-continuity-full-audit/{\"images\":[3,2,1,0],\"m\":4,\"n\":4,\"opens_x\":[[],[3],[2,3],[1,2,3],[0,1,2,3]],\"opens_y\":[[],[3],[1,3],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0050","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-full-audit；資料={\"n\":3,\"m\":3,\"opens_x\":[[],[0],[0,1],[0,1,2]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2]],\"images\":[0,1,2]}。請依 [images,all_target_open_preimage_rows,continuous] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2], [[[], [], 是], [[0], [0], 是], [[1], [1], 否], [[0, 1], [0, 1], 是], [[2], [2], 否], [[0, 2], [0, 2], 否], [[1, 2], [1, 2], 否], [[0, 1, 2], [0, 1, 2], 是]], 否)","explanation_zh":"第二批擴展核對=([0, 1, 2], [[[], [], 是], [[0], [0], 是], [[1], [1], 否], [[0, 1], [0, 1], 是], [[2], [2], 否], [[0, 2], [0, 2], 否], [[1, 2], [1, 2], 否], [[0, 1, 2], [0, 1, 2], 是]], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-full-audit","seed":202610193050,"parameters":{"n":3,"m":3,"opens_x":[[],[0],[0,1],[0,1,2]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2]],"images":[0,1,2],"domain":"Fin_topological_map","operation":"continuity-full-audit","semantic_template":"qf-ext19-continuity-full-audit/{\"images\":[0,1,2],\"m\":3,\"n\":3,\"opens_x\":[[],[0],[0,1],[0,1,2]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0051","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-composition；資料={\"n\":4,\"m\":4,\"k\":4,\"opens_x\":[[],[0],[0,1],[0,1,2],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"opens_z\":[[],[0,1,2,3]],\"images_f\":[0,1,2,3],\"images_g\":[0,1,2,3]}。請依 [f,g,g_after_f,f_continuous,g_continuous,composition_continuous,composition_rows] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3], [0, 1, 2, 3], [0, 1, 2, 3], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])","explanation_zh":"第二批擴展核對=([0, 1, 2, 3], [0, 1, 2, 3], [0, 1, 2, 3], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-composition","seed":202610193051,"parameters":{"n":4,"m":4,"k":4,"opens_x":[[],[0],[0,1],[0,1,2],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"opens_z":[[],[0,1,2,3]],"images_f":[0,1,2,3],"images_g":[0,1,2,3],"domain":"Fin_topological_map","operation":"continuity-composition","semantic_template":"qf-ext19-continuity-composition/{\"images_f\":[0,1,2,3],\"images_g\":[0,1,2,3],\"k\":4,\"m\":4,\"n\":4,\"opens_x\":[[],[0],[0,1],[0,1,2],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"opens_z\":[[],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0052","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-composition；資料={\"n\":4,\"m\":4,\"k\":4,\"opens_x\":[[],[1],[0,1],[0,1,2],[0,1,2,3]],\"opens_y\":[[],[1],[1,2],[0,1,2],[0,1,2,3]],\"opens_z\":[[],[0,1,2,3]],\"images_f\":[1,0,2,3],\"images_g\":[3,1,0,2]}。請依 [f,g,g_after_f,f_continuous,g_continuous,composition_continuous,composition_rows] 欄序回答。","answer":{"kind":"expression","value":"([1, 0, 2, 3], [3, 1, 0, 2], [1, 3, 0, 2], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])","explanation_zh":"第二批擴展核對=([1, 0, 2, 3], [3, 1, 0, 2], [1, 3, 0, 2], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-composition","seed":202610193052,"parameters":{"n":4,"m":4,"k":4,"opens_x":[[],[1],[0,1],[0,1,2],[0,1,2,3]],"opens_y":[[],[1],[1,2],[0,1,2],[0,1,2,3]],"opens_z":[[],[0,1,2,3]],"images_f":[1,0,2,3],"images_g":[3,1,0,2],"domain":"Fin_topological_map","operation":"continuity-composition","semantic_template":"qf-ext19-continuity-composition/{\"images_f\":[1,0,2,3],\"images_g\":[3,1,0,2],\"k\":4,\"m\":4,\"n\":4,\"opens_x\":[[],[1],[0,1],[0,1,2],[0,1,2,3]],\"opens_y\":[[],[1],[1,2],[0,1,2],[0,1,2,3]],\"opens_z\":[[],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0053","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-composition；資料={\"n\":4,\"m\":4,\"k\":4,\"opens_x\":[[],[2],[0,2],[0,1,2],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"opens_z\":[[],[0,1,2,3]],\"images_f\":[2,0,1,3],\"images_g\":[2,0,3,1]}。請依 [f,g,g_after_f,f_continuous,g_continuous,composition_continuous,composition_rows] 欄序回答。","answer":{"kind":"expression","value":"([2, 0, 1, 3], [2, 0, 3, 1], [3, 2, 0, 1], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])","explanation_zh":"第二批擴展核對=([2, 0, 1, 3], [2, 0, 3, 1], [3, 2, 0, 1], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-composition","seed":202610193053,"parameters":{"n":4,"m":4,"k":4,"opens_x":[[],[2],[0,2],[0,1,2],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"opens_z":[[],[0,1,2,3]],"images_f":[2,0,1,3],"images_g":[2,0,3,1],"domain":"Fin_topological_map","operation":"continuity-composition","semantic_template":"qf-ext19-continuity-composition/{\"images_f\":[2,0,1,3],\"images_g\":[2,0,3,1],\"k\":4,\"m\":4,\"n\":4,\"opens_x\":[[],[2],[0,2],[0,1,2],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"opens_z\":[[],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0054","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-composition；資料={\"n\":4,\"m\":4,\"k\":4,\"opens_x\":[[],[3],[0,3],[0,1,3],[0,1,2,3]],\"opens_y\":[[],[3],[0,3],[0,2,3],[0,1,2,3]],\"opens_z\":[[],[0,1,2,3]],\"images_f\":[3,0,1,2],\"images_g\":[1,3,2,0]}。請依 [f,g,g_after_f,f_continuous,g_continuous,composition_continuous,composition_rows] 欄序回答。","answer":{"kind":"expression","value":"([3, 0, 1, 2], [1, 3, 2, 0], [0, 1, 3, 2], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])","explanation_zh":"第二批擴展核對=([3, 0, 1, 2], [1, 3, 2, 0], [0, 1, 3, 2], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-composition","seed":202610193054,"parameters":{"n":4,"m":4,"k":4,"opens_x":[[],[3],[0,3],[0,1,3],[0,1,2,3]],"opens_y":[[],[3],[0,3],[0,2,3],[0,1,2,3]],"opens_z":[[],[0,1,2,3]],"images_f":[3,0,1,2],"images_g":[1,3,2,0],"domain":"Fin_topological_map","operation":"continuity-composition","semantic_template":"qf-ext19-continuity-composition/{\"images_f\":[3,0,1,2],\"images_g\":[1,3,2,0],\"k\":4,\"m\":4,\"n\":4,\"opens_x\":[[],[3],[0,3],[0,1,3],[0,1,2,3]],\"opens_y\":[[],[3],[0,3],[0,2,3],[0,1,2,3]],\"opens_z\":[[],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0055","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-composition；資料={\"n\":4,\"m\":4,\"k\":4,\"opens_x\":[[],[0],[0,2],[0,1,2],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"opens_z\":[[],[0,1,2,3]],\"images_f\":[0,2,1,3],\"images_g\":[0,2,1,3]}。請依 [f,g,g_after_f,f_continuous,g_continuous,composition_continuous,composition_rows] 欄序回答。","answer":{"kind":"expression","value":"([0, 2, 1, 3], [0, 2, 1, 3], [0, 1, 2, 3], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])","explanation_zh":"第二批擴展核對=([0, 2, 1, 3], [0, 2, 1, 3], [0, 1, 2, 3], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-composition","seed":202610193055,"parameters":{"n":4,"m":4,"k":4,"opens_x":[[],[0],[0,2],[0,1,2],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"opens_z":[[],[0,1,2,3]],"images_f":[0,2,1,3],"images_g":[0,2,1,3],"domain":"Fin_topological_map","operation":"continuity-composition","semantic_template":"qf-ext19-continuity-composition/{\"images_f\":[0,2,1,3],\"images_g\":[0,2,1,3],\"k\":4,\"m\":4,\"n\":4,\"opens_x\":[[],[0],[0,2],[0,1,2],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"opens_z\":[[],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0056","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-composition；資料={\"n\":4,\"m\":4,\"k\":4,\"opens_x\":[[],[1],[1,2],[0,1,2],[0,1,2,3]],\"opens_y\":[[],[1],[0,1],[0,1,2],[0,1,2,3]],\"opens_z\":[[],[0,1,2,3]],\"images_f\":[1,2,0,3],\"images_g\":[3,2,0,1]}。請依 [f,g,g_after_f,f_continuous,g_continuous,composition_continuous,composition_rows] 欄序回答。","answer":{"kind":"expression","value":"([1, 2, 0, 3], [3, 2, 0, 1], [2, 0, 3, 1], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])","explanation_zh":"第二批擴展核對=([1, 2, 0, 3], [3, 2, 0, 1], [2, 0, 3, 1], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-composition","seed":202610193056,"parameters":{"n":4,"m":4,"k":4,"opens_x":[[],[1],[1,2],[0,1,2],[0,1,2,3]],"opens_y":[[],[1],[0,1],[0,1,2],[0,1,2,3]],"opens_z":[[],[0,1,2,3]],"images_f":[1,2,0,3],"images_g":[3,2,0,1],"domain":"Fin_topological_map","operation":"continuity-composition","semantic_template":"qf-ext19-continuity-composition/{\"images_f\":[1,2,0,3],\"images_g\":[3,2,0,1],\"k\":4,\"m\":4,\"n\":4,\"opens_x\":[[],[1],[1,2],[0,1,2],[0,1,2,3]],\"opens_y\":[[],[1],[0,1],[0,1,2],[0,1,2,3]],\"opens_z\":[[],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0057","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-composition；資料={\"n\":4,\"m\":4,\"k\":4,\"opens_x\":[[],[2],[1,2],[0,1,2],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"opens_z\":[[],[0,1,2,3]],\"images_f\":[2,1,0,3],\"images_g\":[2,1,3,0]}。請依 [f,g,g_after_f,f_continuous,g_continuous,composition_continuous,composition_rows] 欄序回答。","answer":{"kind":"expression","value":"([2, 1, 0, 3], [2, 1, 3, 0], [3, 1, 2, 0], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])","explanation_zh":"第二批擴展核對=([2, 1, 0, 3], [2, 1, 3, 0], [3, 1, 2, 0], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-composition","seed":202610193057,"parameters":{"n":4,"m":4,"k":4,"opens_x":[[],[2],[1,2],[0,1,2],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"opens_z":[[],[0,1,2,3]],"images_f":[2,1,0,3],"images_g":[2,1,3,0],"domain":"Fin_topological_map","operation":"continuity-composition","semantic_template":"qf-ext19-continuity-composition/{\"images_f\":[2,1,0,3],\"images_g\":[2,1,3,0],\"k\":4,\"m\":4,\"n\":4,\"opens_x\":[[],[2],[1,2],[0,1,2],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"opens_z\":[[],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0058","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-composition；資料={\"n\":4,\"m\":4,\"k\":4,\"opens_x\":[[],[3],[1,3],[0,1,3],[0,1,2,3]],\"opens_y\":[[],[3],[2,3],[0,2,3],[0,1,2,3]],\"opens_z\":[[],[0,1,2,3]],\"images_f\":[3,1,0,2],\"images_g\":[1,0,2,3]}。請依 [f,g,g_after_f,f_continuous,g_continuous,composition_continuous,composition_rows] 欄序回答。","answer":{"kind":"expression","value":"([3, 1, 0, 2], [1, 0, 2, 3], [3, 0, 1, 2], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])","explanation_zh":"第二批擴展核對=([3, 1, 0, 2], [1, 0, 2, 3], [3, 0, 1, 2], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-composition","seed":202610193058,"parameters":{"n":4,"m":4,"k":4,"opens_x":[[],[3],[1,3],[0,1,3],[0,1,2,3]],"opens_y":[[],[3],[2,3],[0,2,3],[0,1,2,3]],"opens_z":[[],[0,1,2,3]],"images_f":[3,1,0,2],"images_g":[1,0,2,3],"domain":"Fin_topological_map","operation":"continuity-composition","semantic_template":"qf-ext19-continuity-composition/{\"images_f\":[3,1,0,2],\"images_g\":[1,0,2,3],\"k\":4,\"m\":4,\"n\":4,\"opens_x\":[[],[3],[1,3],[0,1,3],[0,1,2,3]],\"opens_y\":[[],[3],[2,3],[0,2,3],[0,1,2,3]],\"opens_z\":[[],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0059","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-composition；資料={\"n\":4,\"m\":4,\"k\":4,\"opens_x\":[[],[0],[0,3],[0,1,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"opens_z\":[[],[0,1,2,3]],\"images_f\":[0,3,1,2],\"images_g\":[0,3,1,2]}。請依 [f,g,g_after_f,f_continuous,g_continuous,composition_continuous,composition_rows] 欄序回答。","answer":{"kind":"expression","value":"([0, 3, 1, 2], [0, 3, 1, 2], [0, 2, 3, 1], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])","explanation_zh":"第二批擴展核對=([0, 3, 1, 2], [0, 3, 1, 2], [0, 2, 3, 1], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-composition","seed":202610193059,"parameters":{"n":4,"m":4,"k":4,"opens_x":[[],[0],[0,3],[0,1,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"opens_z":[[],[0,1,2,3]],"images_f":[0,3,1,2],"images_g":[0,3,1,2],"domain":"Fin_topological_map","operation":"continuity-composition","semantic_template":"qf-ext19-continuity-composition/{\"images_f\":[0,3,1,2],\"images_g\":[0,3,1,2],\"k\":4,\"m\":4,\"n\":4,\"opens_x\":[[],[0],[0,3],[0,1,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"opens_z\":[[],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0060","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-composition；資料={\"n\":4,\"m\":4,\"k\":4,\"opens_x\":[[],[1],[1,3],[0,1,3],[0,1,2,3]],\"opens_y\":[[],[1],[1,3],[1,2,3],[0,1,2,3]],\"opens_z\":[[],[0,1,2,3]],\"images_f\":[1,3,0,2],\"images_g\":[3,0,2,1]}。請依 [f,g,g_after_f,f_continuous,g_continuous,composition_continuous,composition_rows] 欄序回答。","answer":{"kind":"expression","value":"([1, 3, 0, 2], [3, 0, 2, 1], [0, 1, 3, 2], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])","explanation_zh":"第二批擴展核對=([1, 3, 0, 2], [3, 0, 2, 1], [0, 1, 3, 2], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-composition","seed":202610193060,"parameters":{"n":4,"m":4,"k":4,"opens_x":[[],[1],[1,3],[0,1,3],[0,1,2,3]],"opens_y":[[],[1],[1,3],[1,2,3],[0,1,2,3]],"opens_z":[[],[0,1,2,3]],"images_f":[1,3,0,2],"images_g":[3,0,2,1],"domain":"Fin_topological_map","operation":"continuity-composition","semantic_template":"qf-ext19-continuity-composition/{\"images_f\":[1,3,0,2],\"images_g\":[3,0,2,1],\"k\":4,\"m\":4,\"n\":4,\"opens_x\":[[],[1],[1,3],[0,1,3],[0,1,2,3]],\"opens_y\":[[],[1],[1,3],[1,2,3],[0,1,2,3]],\"opens_z\":[[],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0061","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-composition；資料={\"n\":4,\"m\":4,\"k\":4,\"opens_x\":[[],[2],[2,3],[0,2,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"opens_z\":[[],[0,1,2,3]],\"images_f\":[2,3,0,1],\"images_g\":[2,3,1,0]}。請依 [f,g,g_after_f,f_continuous,g_continuous,composition_continuous,composition_rows] 欄序回答。","answer":{"kind":"expression","value":"([2, 3, 0, 1], [2, 3, 1, 0], [1, 0, 2, 3], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])","explanation_zh":"第二批擴展核對=([2, 3, 0, 1], [2, 3, 1, 0], [1, 0, 2, 3], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-composition","seed":202610193061,"parameters":{"n":4,"m":4,"k":4,"opens_x":[[],[2],[2,3],[0,2,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"opens_z":[[],[0,1,2,3]],"images_f":[2,3,0,1],"images_g":[2,3,1,0],"domain":"Fin_topological_map","operation":"continuity-composition","semantic_template":"qf-ext19-continuity-composition/{\"images_f\":[2,3,0,1],\"images_g\":[2,3,1,0],\"k\":4,\"m\":4,\"n\":4,\"opens_x\":[[],[2],[2,3],[0,2,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"opens_z\":[[],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0062","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-composition；資料={\"n\":4,\"m\":4,\"k\":4,\"opens_x\":[[],[3],[2,3],[0,2,3],[0,1,2,3]],\"opens_y\":[[],[3],[1,3],[0,1,3],[0,1,2,3]],\"opens_z\":[[],[0,1,2,3]],\"images_f\":[3,2,0,1],\"images_g\":[1,2,0,3]}。請依 [f,g,g_after_f,f_continuous,g_continuous,composition_continuous,composition_rows] 欄序回答。","answer":{"kind":"expression","value":"([3, 2, 0, 1], [1, 2, 0, 3], [3, 0, 1, 2], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])","explanation_zh":"第二批擴展核對=([3, 2, 0, 1], [1, 2, 0, 3], [3, 0, 1, 2], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-composition","seed":202610193062,"parameters":{"n":4,"m":4,"k":4,"opens_x":[[],[3],[2,3],[0,2,3],[0,1,2,3]],"opens_y":[[],[3],[1,3],[0,1,3],[0,1,2,3]],"opens_z":[[],[0,1,2,3]],"images_f":[3,2,0,1],"images_g":[1,2,0,3],"domain":"Fin_topological_map","operation":"continuity-composition","semantic_template":"qf-ext19-continuity-composition/{\"images_f\":[3,2,0,1],\"images_g\":[1,2,0,3],\"k\":4,\"m\":4,\"n\":4,\"opens_x\":[[],[3],[2,3],[0,2,3],[0,1,2,3]],\"opens_y\":[[],[3],[1,3],[0,1,3],[0,1,2,3]],\"opens_z\":[[],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0063","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-composition；資料={\"n\":4,\"m\":4,\"k\":4,\"opens_x\":[[],[0],[0,1],[0,1,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"opens_z\":[[],[0,1,2,3]],\"images_f\":[0,1,3,2],\"images_g\":[0,1,3,2]}。請依 [f,g,g_after_f,f_continuous,g_continuous,composition_continuous,composition_rows] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 3, 2], [0, 1, 3, 2], [0, 1, 2, 3], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])","explanation_zh":"第二批擴展核對=([0, 1, 3, 2], [0, 1, 3, 2], [0, 1, 2, 3], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-composition","seed":202610193063,"parameters":{"n":4,"m":4,"k":4,"opens_x":[[],[0],[0,1],[0,1,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"opens_z":[[],[0,1,2,3]],"images_f":[0,1,3,2],"images_g":[0,1,3,2],"domain":"Fin_topological_map","operation":"continuity-composition","semantic_template":"qf-ext19-continuity-composition/{\"images_f\":[0,1,3,2],\"images_g\":[0,1,3,2],\"k\":4,\"m\":4,\"n\":4,\"opens_x\":[[],[0],[0,1],[0,1,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"opens_z\":[[],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0064","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-composition；資料={\"n\":4,\"m\":4,\"k\":4,\"opens_x\":[[],[1],[0,1],[0,1,3],[0,1,2,3]],\"opens_y\":[[],[1],[1,2],[1,2,3],[0,1,2,3]],\"opens_z\":[[],[0,1,2,3]],\"images_f\":[1,0,3,2],\"images_g\":[3,1,2,0]}。請依 [f,g,g_after_f,f_continuous,g_continuous,composition_continuous,composition_rows] 欄序回答。","answer":{"kind":"expression","value":"([1, 0, 3, 2], [3, 1, 2, 0], [1, 3, 0, 2], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])","explanation_zh":"第二批擴展核對=([1, 0, 3, 2], [3, 1, 2, 0], [1, 3, 0, 2], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-composition","seed":202610193064,"parameters":{"n":4,"m":4,"k":4,"opens_x":[[],[1],[0,1],[0,1,3],[0,1,2,3]],"opens_y":[[],[1],[1,2],[1,2,3],[0,1,2,3]],"opens_z":[[],[0,1,2,3]],"images_f":[1,0,3,2],"images_g":[3,1,2,0],"domain":"Fin_topological_map","operation":"continuity-composition","semantic_template":"qf-ext19-continuity-composition/{\"images_f\":[1,0,3,2],\"images_g\":[3,1,2,0],\"k\":4,\"m\":4,\"n\":4,\"opens_x\":[[],[1],[0,1],[0,1,3],[0,1,2,3]],\"opens_y\":[[],[1],[1,2],[1,2,3],[0,1,2,3]],\"opens_z\":[[],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0065","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-composition；資料={\"n\":4,\"m\":4,\"k\":4,\"opens_x\":[[],[2],[0,2],[0,2,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"opens_z\":[[],[0,1,2,3]],\"images_f\":[2,0,3,1],\"images_g\":[2,0,1,3]}。請依 [f,g,g_after_f,f_continuous,g_continuous,composition_continuous,composition_rows] 欄序回答。","answer":{"kind":"expression","value":"([2, 0, 3, 1], [2, 0, 1, 3], [1, 2, 3, 0], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])","explanation_zh":"第二批擴展核對=([2, 0, 3, 1], [2, 0, 1, 3], [1, 2, 3, 0], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-composition","seed":202610193065,"parameters":{"n":4,"m":4,"k":4,"opens_x":[[],[2],[0,2],[0,2,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"opens_z":[[],[0,1,2,3]],"images_f":[2,0,3,1],"images_g":[2,0,1,3],"domain":"Fin_topological_map","operation":"continuity-composition","semantic_template":"qf-ext19-continuity-composition/{\"images_f\":[2,0,3,1],\"images_g\":[2,0,1,3],\"k\":4,\"m\":4,\"n\":4,\"opens_x\":[[],[2],[0,2],[0,2,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"opens_z\":[[],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0066","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-composition；資料={\"n\":4,\"m\":4,\"k\":4,\"opens_x\":[[],[3],[0,3],[0,2,3],[0,1,2,3]],\"opens_y\":[[],[3],[0,3],[0,1,3],[0,1,2,3]],\"opens_z\":[[],[0,1,2,3]],\"images_f\":[3,0,2,1],\"images_g\":[1,3,0,2]}。請依 [f,g,g_after_f,f_continuous,g_continuous,composition_continuous,composition_rows] 欄序回答。","answer":{"kind":"expression","value":"([3, 0, 2, 1], [1, 3, 0, 2], [2, 1, 0, 3], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])","explanation_zh":"第二批擴展核對=([3, 0, 2, 1], [1, 3, 0, 2], [2, 1, 0, 3], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-composition","seed":202610193066,"parameters":{"n":4,"m":4,"k":4,"opens_x":[[],[3],[0,3],[0,2,3],[0,1,2,3]],"opens_y":[[],[3],[0,3],[0,1,3],[0,1,2,3]],"opens_z":[[],[0,1,2,3]],"images_f":[3,0,2,1],"images_g":[1,3,0,2],"domain":"Fin_topological_map","operation":"continuity-composition","semantic_template":"qf-ext19-continuity-composition/{\"images_f\":[3,0,2,1],\"images_g\":[1,3,0,2],\"k\":4,\"m\":4,\"n\":4,\"opens_x\":[[],[3],[0,3],[0,2,3],[0,1,2,3]],\"opens_y\":[[],[3],[0,3],[0,1,3],[0,1,2,3]],\"opens_z\":[[],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0067","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-composition；資料={\"n\":4,\"m\":4,\"k\":4,\"opens_x\":[[],[0],[0,2],[0,2,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"opens_z\":[[],[0,1,2,3]],\"images_f\":[0,2,3,1],\"images_g\":[0,2,3,1]}。請依 [f,g,g_after_f,f_continuous,g_continuous,composition_continuous,composition_rows] 欄序回答。","answer":{"kind":"expression","value":"([0, 2, 3, 1], [0, 2, 3, 1], [0, 3, 1, 2], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])","explanation_zh":"第二批擴展核對=([0, 2, 3, 1], [0, 2, 3, 1], [0, 3, 1, 2], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-composition","seed":202610193067,"parameters":{"n":4,"m":4,"k":4,"opens_x":[[],[0],[0,2],[0,2,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"opens_z":[[],[0,1,2,3]],"images_f":[0,2,3,1],"images_g":[0,2,3,1],"domain":"Fin_topological_map","operation":"continuity-composition","semantic_template":"qf-ext19-continuity-composition/{\"images_f\":[0,2,3,1],\"images_g\":[0,2,3,1],\"k\":4,\"m\":4,\"n\":4,\"opens_x\":[[],[0],[0,2],[0,2,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"opens_z\":[[],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0068","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-composition；資料={\"n\":4,\"m\":4,\"k\":4,\"opens_x\":[[],[1],[1,2],[1,2,3],[0,1,2,3]],\"opens_y\":[[],[1],[0,1],[0,1,3],[0,1,2,3]],\"opens_z\":[[],[0,1,2,3]],\"images_f\":[1,2,3,0],\"images_g\":[3,2,1,0]}。請依 [f,g,g_after_f,f_continuous,g_continuous,composition_continuous,composition_rows] 欄序回答。","answer":{"kind":"expression","value":"([1, 2, 3, 0], [3, 2, 1, 0], [2, 1, 0, 3], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])","explanation_zh":"第二批擴展核對=([1, 2, 3, 0], [3, 2, 1, 0], [2, 1, 0, 3], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-composition","seed":202610193068,"parameters":{"n":4,"m":4,"k":4,"opens_x":[[],[1],[1,2],[1,2,3],[0,1,2,3]],"opens_y":[[],[1],[0,1],[0,1,3],[0,1,2,3]],"opens_z":[[],[0,1,2,3]],"images_f":[1,2,3,0],"images_g":[3,2,1,0],"domain":"Fin_topological_map","operation":"continuity-composition","semantic_template":"qf-ext19-continuity-composition/{\"images_f\":[1,2,3,0],\"images_g\":[3,2,1,0],\"k\":4,\"m\":4,\"n\":4,\"opens_x\":[[],[1],[1,2],[1,2,3],[0,1,2,3]],\"opens_y\":[[],[1],[0,1],[0,1,3],[0,1,2,3]],\"opens_z\":[[],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0069","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-composition；資料={\"n\":4,\"m\":4,\"k\":4,\"opens_x\":[[],[2],[1,2],[1,2,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"opens_z\":[[],[0,1,2,3]],\"images_f\":[2,1,3,0],\"images_g\":[2,1,0,3]}。請依 [f,g,g_after_f,f_continuous,g_continuous,composition_continuous,composition_rows] 欄序回答。","answer":{"kind":"expression","value":"([2, 1, 3, 0], [2, 1, 0, 3], [0, 1, 3, 2], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])","explanation_zh":"第二批擴展核對=([2, 1, 3, 0], [2, 1, 0, 3], [0, 1, 3, 2], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-composition","seed":202610193069,"parameters":{"n":4,"m":4,"k":4,"opens_x":[[],[2],[1,2],[1,2,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"opens_z":[[],[0,1,2,3]],"images_f":[2,1,3,0],"images_g":[2,1,0,3],"domain":"Fin_topological_map","operation":"continuity-composition","semantic_template":"qf-ext19-continuity-composition/{\"images_f\":[2,1,3,0],\"images_g\":[2,1,0,3],\"k\":4,\"m\":4,\"n\":4,\"opens_x\":[[],[2],[1,2],[1,2,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"opens_z\":[[],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0070","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-composition；資料={\"n\":4,\"m\":4,\"k\":4,\"opens_x\":[[],[3],[1,3],[1,2,3],[0,1,2,3]],\"opens_y\":[[],[3],[2,3],[1,2,3],[0,1,2,3]],\"opens_z\":[[],[0,1,2,3]],\"images_f\":[3,1,2,0],\"images_g\":[1,0,3,2]}。請依 [f,g,g_after_f,f_continuous,g_continuous,composition_continuous,composition_rows] 欄序回答。","answer":{"kind":"expression","value":"([3, 1, 2, 0], [1, 0, 3, 2], [2, 0, 3, 1], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])","explanation_zh":"第二批擴展核對=([3, 1, 2, 0], [1, 0, 3, 2], [2, 0, 3, 1], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-composition","seed":202610193070,"parameters":{"n":4,"m":4,"k":4,"opens_x":[[],[3],[1,3],[1,2,3],[0,1,2,3]],"opens_y":[[],[3],[2,3],[1,2,3],[0,1,2,3]],"opens_z":[[],[0,1,2,3]],"images_f":[3,1,2,0],"images_g":[1,0,3,2],"domain":"Fin_topological_map","operation":"continuity-composition","semantic_template":"qf-ext19-continuity-composition/{\"images_f\":[3,1,2,0],\"images_g\":[1,0,3,2],\"k\":4,\"m\":4,\"n\":4,\"opens_x\":[[],[3],[1,3],[1,2,3],[0,1,2,3]],\"opens_y\":[[],[3],[2,3],[1,2,3],[0,1,2,3]],\"opens_z\":[[],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0071","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-composition；資料={\"n\":4,\"m\":4,\"k\":4,\"opens_x\":[[],[0],[0,3],[0,2,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"opens_z\":[[],[0,1,2,3]],\"images_f\":[0,3,2,1],\"images_g\":[0,3,2,1]}。請依 [f,g,g_after_f,f_continuous,g_continuous,composition_continuous,composition_rows] 欄序回答。","answer":{"kind":"expression","value":"([0, 3, 2, 1], [0, 3, 2, 1], [0, 1, 2, 3], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])","explanation_zh":"第二批擴展核對=([0, 3, 2, 1], [0, 3, 2, 1], [0, 1, 2, 3], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-composition","seed":202610193071,"parameters":{"n":4,"m":4,"k":4,"opens_x":[[],[0],[0,3],[0,2,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"opens_z":[[],[0,1,2,3]],"images_f":[0,3,2,1],"images_g":[0,3,2,1],"domain":"Fin_topological_map","operation":"continuity-composition","semantic_template":"qf-ext19-continuity-composition/{\"images_f\":[0,3,2,1],\"images_g\":[0,3,2,1],\"k\":4,\"m\":4,\"n\":4,\"opens_x\":[[],[0],[0,3],[0,2,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"opens_z\":[[],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0072","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-composition；資料={\"n\":4,\"m\":4,\"k\":4,\"opens_x\":[[],[1],[1,3],[1,2,3],[0,1,2,3]],\"opens_y\":[[],[1],[1,3],[0,1,3],[0,1,2,3]],\"opens_z\":[[],[0,1,2,3]],\"images_f\":[1,3,2,0],\"images_g\":[3,0,1,2]}。請依 [f,g,g_after_f,f_continuous,g_continuous,composition_continuous,composition_rows] 欄序回答。","answer":{"kind":"expression","value":"([1, 3, 2, 0], [3, 0, 1, 2], [0, 2, 1, 3], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])","explanation_zh":"第二批擴展核對=([1, 3, 2, 0], [3, 0, 1, 2], [0, 2, 1, 3], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-composition","seed":202610193072,"parameters":{"n":4,"m":4,"k":4,"opens_x":[[],[1],[1,3],[1,2,3],[0,1,2,3]],"opens_y":[[],[1],[1,3],[0,1,3],[0,1,2,3]],"opens_z":[[],[0,1,2,3]],"images_f":[1,3,2,0],"images_g":[3,0,1,2],"domain":"Fin_topological_map","operation":"continuity-composition","semantic_template":"qf-ext19-continuity-composition/{\"images_f\":[1,3,2,0],\"images_g\":[3,0,1,2],\"k\":4,\"m\":4,\"n\":4,\"opens_x\":[[],[1],[1,3],[1,2,3],[0,1,2,3]],\"opens_y\":[[],[1],[1,3],[0,1,3],[0,1,2,3]],\"opens_z\":[[],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0073","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-composition；資料={\"n\":4,\"m\":4,\"k\":4,\"opens_x\":[[],[2],[2,3],[1,2,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"opens_z\":[[],[0,1,2,3]],\"images_f\":[2,3,1,0],\"images_g\":[2,3,0,1]}。請依 [f,g,g_after_f,f_continuous,g_continuous,composition_continuous,composition_rows] 欄序回答。","answer":{"kind":"expression","value":"([2, 3, 1, 0], [2, 3, 0, 1], [0, 1, 3, 2], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])","explanation_zh":"第二批擴展核對=([2, 3, 1, 0], [2, 3, 0, 1], [0, 1, 3, 2], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-composition","seed":202610193073,"parameters":{"n":4,"m":4,"k":4,"opens_x":[[],[2],[2,3],[1,2,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"opens_z":[[],[0,1,2,3]],"images_f":[2,3,1,0],"images_g":[2,3,0,1],"domain":"Fin_topological_map","operation":"continuity-composition","semantic_template":"qf-ext19-continuity-composition/{\"images_f\":[2,3,1,0],\"images_g\":[2,3,0,1],\"k\":4,\"m\":4,\"n\":4,\"opens_x\":[[],[2],[2,3],[1,2,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"opens_z\":[[],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0074","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-composition；資料={\"n\":4,\"m\":4,\"k\":4,\"opens_x\":[[],[3],[2,3],[1,2,3],[0,1,2,3]],\"opens_y\":[[],[3],[1,3],[1,2,3],[0,1,2,3]],\"opens_z\":[[],[0,1,2,3]],\"images_f\":[3,2,1,0],\"images_g\":[1,2,3,0]}。請依 [f,g,g_after_f,f_continuous,g_continuous,composition_continuous,composition_rows] 欄序回答。","answer":{"kind":"expression","value":"([3, 2, 1, 0], [1, 2, 3, 0], [0, 3, 2, 1], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])","explanation_zh":"第二批擴展核對=([3, 2, 1, 0], [1, 2, 3, 0], [0, 3, 2, 1], 否, 是, 是, [[[], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-composition","seed":202610193074,"parameters":{"n":4,"m":4,"k":4,"opens_x":[[],[3],[2,3],[1,2,3],[0,1,2,3]],"opens_y":[[],[3],[1,3],[1,2,3],[0,1,2,3]],"opens_z":[[],[0,1,2,3]],"images_f":[3,2,1,0],"images_g":[1,2,3,0],"domain":"Fin_topological_map","operation":"continuity-composition","semantic_template":"qf-ext19-continuity-composition/{\"images_f\":[3,2,1,0],\"images_g\":[1,2,3,0],\"k\":4,\"m\":4,\"n\":4,\"opens_x\":[[],[3],[2,3],[1,2,3],[0,1,2,3]],\"opens_y\":[[],[3],[1,3],[1,2,3],[0,1,2,3]],\"opens_z\":[[],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0075","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-composition；資料={\"n\":3,\"m\":3,\"k\":3,\"opens_x\":[[],[0],[0,1],[0,1,2]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2]],\"opens_z\":[[],[0,1,2]],\"images_f\":[0,1,2],\"images_g\":[0,1,2]}。請依 [f,g,g_after_f,f_continuous,g_continuous,composition_continuous,composition_rows] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2], [0, 1, 2], [0, 1, 2], 否, 是, 是, [[[], [], 是], [[0, 1, 2], [0, 1, 2], 是]])","explanation_zh":"第二批擴展核對=([0, 1, 2], [0, 1, 2], [0, 1, 2], 否, 是, 是, [[[], [], 是], [[0, 1, 2], [0, 1, 2], 是]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-composition","seed":202610193075,"parameters":{"n":3,"m":3,"k":3,"opens_x":[[],[0],[0,1],[0,1,2]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2]],"opens_z":[[],[0,1,2]],"images_f":[0,1,2],"images_g":[0,1,2],"domain":"Fin_topological_map","operation":"continuity-composition","semantic_template":"qf-ext19-continuity-composition/{\"images_f\":[0,1,2],\"images_g\":[0,1,2],\"k\":3,\"m\":3,\"n\":3,\"opens_x\":[[],[0],[0,1],[0,1,2]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2]],\"opens_z\":[[],[0,1,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0076","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-open-map-contrast；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[0],[0,1],[0,1,2],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"images\":[0,1,2,3]}。請依 [images,continuous,open_map,preimage_rows,image_rows,comparison] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3], 否, 是, [[[], [], 是], [[0], [0], 是], [[1], [1], 否], [[0, 1], [0, 1], 是], [[2], [2], 否], [[0, 2], [0, 2], 否], [[1, 2], [1, 2], 否], [[0, 1, 2], [0, 1, 2], 是], [[3], [3], 否], [[0, 3], [0, 3], 否], [[1, 3], [1, 3], 否], [[0, 1, 3], [0, 1, 3], 否], [[2, 3], [2, 3], 否], [[0, 2, 3], [0, 2, 3], 否], [[1, 2, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[0], [0], 是], [[0, 1], [0, 1], 是], [[0, 1, 2], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 性質不同)","explanation_zh":"第二批擴展核對=([0, 1, 2, 3], 否, 是, [[[], [], 是], [[0], [0], 是], [[1], [1], 否], [[0, 1], [0, 1], 是], [[2], [2], 否], [[0, 2], [0, 2], 否], [[1, 2], [1, 2], 否], [[0, 1, 2], [0, 1, 2], 是], [[3], [3], 否], [[0, 3], [0, 3], 否], [[1, 3], [1, 3], 否], [[0, 1, 3], [0, 1, 3], 否], [[2, 3], [2, 3], 否], [[0, 2, 3], [0, 2, 3], 否], [[1, 2, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[0], [0], 是], [[0, 1], [0, 1], 是], [[0, 1, 2], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 性質不同)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-open-map-contrast","seed":202610193076,"parameters":{"n":4,"m":4,"opens_x":[[],[0],[0,1],[0,1,2],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[0,1,2,3],"domain":"Fin_topological_map","operation":"continuity-open-map-contrast","semantic_template":"qf-ext19-continuity-open-map-contrast/{\"images\":[0,1,2,3],\"m\":4,\"n\":4,\"opens_x\":[[],[0],[0,1],[0,1,2],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0077","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-open-map-contrast；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[1],[0,1],[0,1,2],[0,1,2,3]],\"opens_y\":[[],[1],[1,2],[0,1,2],[0,1,2,3]],\"images\":[1,0,2,3]}。請依 [images,continuous,open_map,preimage_rows,image_rows,comparison] 欄序回答。","answer":{"kind":"expression","value":"([1, 0, 2, 3], 否, 否, [[[], [], 是], [[1], [0], 否], [[1, 2], [0, 2], 否], [[0, 1, 2], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[1], [0], 否], [[0, 1], [0, 1], 否], [[0, 1, 2], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 同值但責任不同)","explanation_zh":"第二批擴展核對=([1, 0, 2, 3], 否, 否, [[[], [], 是], [[1], [0], 否], [[1, 2], [0, 2], 否], [[0, 1, 2], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[1], [0], 否], [[0, 1], [0, 1], 否], [[0, 1, 2], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 同值但責任不同)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-open-map-contrast","seed":202610193077,"parameters":{"n":4,"m":4,"opens_x":[[],[1],[0,1],[0,1,2],[0,1,2,3]],"opens_y":[[],[1],[1,2],[0,1,2],[0,1,2,3]],"images":[1,0,2,3],"domain":"Fin_topological_map","operation":"continuity-open-map-contrast","semantic_template":"qf-ext19-continuity-open-map-contrast/{\"images\":[1,0,2,3],\"m\":4,\"n\":4,\"opens_x\":[[],[1],[0,1],[0,1,2],[0,1,2,3]],\"opens_y\":[[],[1],[1,2],[0,1,2],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0078","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-open-map-contrast；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[2],[0,2],[0,1,2],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"images\":[2,0,1,3]}。請依 [images,continuous,open_map,preimage_rows,image_rows,comparison] 欄序回答。","answer":{"kind":"expression","value":"([2, 0, 1, 3], 否, 是, [[[], [], 是], [[0], [1], 否], [[1], [2], 是], [[0, 1], [1, 2], 否], [[2], [0], 否], [[0, 2], [0, 1], 否], [[1, 2], [0, 2], 是], [[0, 1, 2], [0, 1, 2], 是], [[3], [3], 否], [[0, 3], [1, 3], 否], [[1, 3], [2, 3], 否], [[0, 1, 3], [1, 2, 3], 否], [[2, 3], [0, 3], 否], [[0, 2, 3], [0, 1, 3], 否], [[1, 2, 3], [0, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[2], [1], 是], [[0, 2], [1, 2], 是], [[0, 1, 2], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 性質不同)","explanation_zh":"第二批擴展核對=([2, 0, 1, 3], 否, 是, [[[], [], 是], [[0], [1], 否], [[1], [2], 是], [[0, 1], [1, 2], 否], [[2], [0], 否], [[0, 2], [0, 1], 否], [[1, 2], [0, 2], 是], [[0, 1, 2], [0, 1, 2], 是], [[3], [3], 否], [[0, 3], [1, 3], 否], [[1, 3], [2, 3], 否], [[0, 1, 3], [1, 2, 3], 否], [[2, 3], [0, 3], 否], [[0, 2, 3], [0, 1, 3], 否], [[1, 2, 3], [0, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[2], [1], 是], [[0, 2], [1, 2], 是], [[0, 1, 2], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 性質不同)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-open-map-contrast","seed":202610193078,"parameters":{"n":4,"m":4,"opens_x":[[],[2],[0,2],[0,1,2],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[2,0,1,3],"domain":"Fin_topological_map","operation":"continuity-open-map-contrast","semantic_template":"qf-ext19-continuity-open-map-contrast/{\"images\":[2,0,1,3],\"m\":4,\"n\":4,\"opens_x\":[[],[2],[0,2],[0,1,2],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0079","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-open-map-contrast；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[3],[0,3],[0,1,3],[0,1,2,3]],\"opens_y\":[[],[3],[0,3],[0,2,3],[0,1,2,3]],\"images\":[3,0,1,2]}。請依 [images,continuous,open_map,preimage_rows,image_rows,comparison] 欄序回答。","answer":{"kind":"expression","value":"([3, 0, 1, 2], 否, 否, [[[], [], 是], [[3], [0], 否], [[0, 3], [0, 1], 否], [[0, 2, 3], [0, 1, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[3], [2], 否], [[0, 3], [2, 3], 否], [[0, 1, 3], [0, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 同值但責任不同)","explanation_zh":"第二批擴展核對=([3, 0, 1, 2], 否, 否, [[[], [], 是], [[3], [0], 否], [[0, 3], [0, 1], 否], [[0, 2, 3], [0, 1, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[3], [2], 否], [[0, 3], [2, 3], 否], [[0, 1, 3], [0, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 同值但責任不同)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-open-map-contrast","seed":202610193079,"parameters":{"n":4,"m":4,"opens_x":[[],[3],[0,3],[0,1,3],[0,1,2,3]],"opens_y":[[],[3],[0,3],[0,2,3],[0,1,2,3]],"images":[3,0,1,2],"domain":"Fin_topological_map","operation":"continuity-open-map-contrast","semantic_template":"qf-ext19-continuity-open-map-contrast/{\"images\":[3,0,1,2],\"m\":4,\"n\":4,\"opens_x\":[[],[3],[0,3],[0,1,3],[0,1,2,3]],\"opens_y\":[[],[3],[0,3],[0,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0080","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-open-map-contrast；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[0],[0,2],[0,1,2],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"images\":[0,2,1,3]}。請依 [images,continuous,open_map,preimage_rows,image_rows,comparison] 欄序回答。","answer":{"kind":"expression","value":"([0, 2, 1, 3], 否, 是, [[[], [], 是], [[0], [0], 是], [[1], [2], 否], [[0, 1], [0, 2], 是], [[2], [1], 否], [[0, 2], [0, 1], 否], [[1, 2], [1, 2], 否], [[0, 1, 2], [0, 1, 2], 是], [[3], [3], 否], [[0, 3], [0, 3], 否], [[1, 3], [2, 3], 否], [[0, 1, 3], [0, 2, 3], 否], [[2, 3], [1, 3], 否], [[0, 2, 3], [0, 1, 3], 否], [[1, 2, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[0], [0], 是], [[0, 2], [0, 1], 是], [[0, 1, 2], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 性質不同)","explanation_zh":"第二批擴展核對=([0, 2, 1, 3], 否, 是, [[[], [], 是], [[0], [0], 是], [[1], [2], 否], [[0, 1], [0, 2], 是], [[2], [1], 否], [[0, 2], [0, 1], 否], [[1, 2], [1, 2], 否], [[0, 1, 2], [0, 1, 2], 是], [[3], [3], 否], [[0, 3], [0, 3], 否], [[1, 3], [2, 3], 否], [[0, 1, 3], [0, 2, 3], 否], [[2, 3], [1, 3], 否], [[0, 2, 3], [0, 1, 3], 否], [[1, 2, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[0], [0], 是], [[0, 2], [0, 1], 是], [[0, 1, 2], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 性質不同)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-open-map-contrast","seed":202610193080,"parameters":{"n":4,"m":4,"opens_x":[[],[0],[0,2],[0,1,2],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[0,2,1,3],"domain":"Fin_topological_map","operation":"continuity-open-map-contrast","semantic_template":"qf-ext19-continuity-open-map-contrast/{\"images\":[0,2,1,3],\"m\":4,\"n\":4,\"opens_x\":[[],[0],[0,2],[0,1,2],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0081","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-open-map-contrast；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[1],[1,2],[0,1,2],[0,1,2,3]],\"opens_y\":[[],[1],[0,1],[0,1,2],[0,1,2,3]],\"images\":[1,2,0,3]}。請依 [images,continuous,open_map,preimage_rows,image_rows,comparison] 欄序回答。","answer":{"kind":"expression","value":"([1, 2, 0, 3], 否, 否, [[[], [], 是], [[1], [0], 否], [[0, 1], [0, 2], 否], [[0, 1, 2], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[1], [2], 否], [[1, 2], [0, 2], 否], [[0, 1, 2], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 同值但責任不同)","explanation_zh":"第二批擴展核對=([1, 2, 0, 3], 否, 否, [[[], [], 是], [[1], [0], 否], [[0, 1], [0, 2], 否], [[0, 1, 2], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[1], [2], 否], [[1, 2], [0, 2], 否], [[0, 1, 2], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 同值但責任不同)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-open-map-contrast","seed":202610193081,"parameters":{"n":4,"m":4,"opens_x":[[],[1],[1,2],[0,1,2],[0,1,2,3]],"opens_y":[[],[1],[0,1],[0,1,2],[0,1,2,3]],"images":[1,2,0,3],"domain":"Fin_topological_map","operation":"continuity-open-map-contrast","semantic_template":"qf-ext19-continuity-open-map-contrast/{\"images\":[1,2,0,3],\"m\":4,\"n\":4,\"opens_x\":[[],[1],[1,2],[0,1,2],[0,1,2,3]],\"opens_y\":[[],[1],[0,1],[0,1,2],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0082","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-open-map-contrast；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[2],[1,2],[0,1,2],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"images\":[2,1,0,3]}。請依 [images,continuous,open_map,preimage_rows,image_rows,comparison] 欄序回答。","answer":{"kind":"expression","value":"([2, 1, 0, 3], 否, 是, [[[], [], 是], [[0], [2], 是], [[1], [1], 否], [[0, 1], [1, 2], 是], [[2], [0], 否], [[0, 2], [0, 2], 否], [[1, 2], [0, 1], 否], [[0, 1, 2], [0, 1, 2], 是], [[3], [3], 否], [[0, 3], [2, 3], 否], [[1, 3], [1, 3], 否], [[0, 1, 3], [1, 2, 3], 否], [[2, 3], [0, 3], 否], [[0, 2, 3], [0, 2, 3], 否], [[1, 2, 3], [0, 1, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[2], [0], 是], [[1, 2], [0, 1], 是], [[0, 1, 2], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 性質不同)","explanation_zh":"第二批擴展核對=([2, 1, 0, 3], 否, 是, [[[], [], 是], [[0], [2], 是], [[1], [1], 否], [[0, 1], [1, 2], 是], [[2], [0], 否], [[0, 2], [0, 2], 否], [[1, 2], [0, 1], 否], [[0, 1, 2], [0, 1, 2], 是], [[3], [3], 否], [[0, 3], [2, 3], 否], [[1, 3], [1, 3], 否], [[0, 1, 3], [1, 2, 3], 否], [[2, 3], [0, 3], 否], [[0, 2, 3], [0, 2, 3], 否], [[1, 2, 3], [0, 1, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[2], [0], 是], [[1, 2], [0, 1], 是], [[0, 1, 2], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 性質不同)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-open-map-contrast","seed":202610193082,"parameters":{"n":4,"m":4,"opens_x":[[],[2],[1,2],[0,1,2],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[2,1,0,3],"domain":"Fin_topological_map","operation":"continuity-open-map-contrast","semantic_template":"qf-ext19-continuity-open-map-contrast/{\"images\":[2,1,0,3],\"m\":4,\"n\":4,\"opens_x\":[[],[2],[1,2],[0,1,2],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0083","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-open-map-contrast；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[3],[1,3],[0,1,3],[0,1,2,3]],\"opens_y\":[[],[3],[2,3],[0,2,3],[0,1,2,3]],\"images\":[3,1,0,2]}。請依 [images,continuous,open_map,preimage_rows,image_rows,comparison] 欄序回答。","answer":{"kind":"expression","value":"([3, 1, 0, 2], 否, 否, [[[], [], 是], [[3], [0], 否], [[2, 3], [0, 3], 否], [[0, 2, 3], [0, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[3], [2], 否], [[1, 3], [1, 2], 否], [[0, 1, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 同值但責任不同)","explanation_zh":"第二批擴展核對=([3, 1, 0, 2], 否, 否, [[[], [], 是], [[3], [0], 否], [[2, 3], [0, 3], 否], [[0, 2, 3], [0, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[3], [2], 否], [[1, 3], [1, 2], 否], [[0, 1, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 同值但責任不同)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-open-map-contrast","seed":202610193083,"parameters":{"n":4,"m":4,"opens_x":[[],[3],[1,3],[0,1,3],[0,1,2,3]],"opens_y":[[],[3],[2,3],[0,2,3],[0,1,2,3]],"images":[3,1,0,2],"domain":"Fin_topological_map","operation":"continuity-open-map-contrast","semantic_template":"qf-ext19-continuity-open-map-contrast/{\"images\":[3,1,0,2],\"m\":4,\"n\":4,\"opens_x\":[[],[3],[1,3],[0,1,3],[0,1,2,3]],\"opens_y\":[[],[3],[2,3],[0,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0084","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-open-map-contrast；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[0],[0,3],[0,1,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"images\":[0,3,1,2]}。請依 [images,continuous,open_map,preimage_rows,image_rows,comparison] 欄序回答。","answer":{"kind":"expression","value":"([0, 3, 1, 2], 否, 是, [[[], [], 是], [[0], [0], 是], [[1], [2], 否], [[0, 1], [0, 2], 否], [[2], [3], 否], [[0, 2], [0, 3], 是], [[1, 2], [2, 3], 否], [[0, 1, 2], [0, 2, 3], 否], [[3], [1], 否], [[0, 3], [0, 1], 否], [[1, 3], [1, 2], 否], [[0, 1, 3], [0, 1, 2], 否], [[2, 3], [1, 3], 否], [[0, 2, 3], [0, 1, 3], 是], [[1, 2, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[0], [0], 是], [[0, 3], [0, 2], 是], [[0, 1, 3], [0, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 性質不同)","explanation_zh":"第二批擴展核對=([0, 3, 1, 2], 否, 是, [[[], [], 是], [[0], [0], 是], [[1], [2], 否], [[0, 1], [0, 2], 否], [[2], [3], 否], [[0, 2], [0, 3], 是], [[1, 2], [2, 3], 否], [[0, 1, 2], [0, 2, 3], 否], [[3], [1], 否], [[0, 3], [0, 1], 否], [[1, 3], [1, 2], 否], [[0, 1, 3], [0, 1, 2], 否], [[2, 3], [1, 3], 否], [[0, 2, 3], [0, 1, 3], 是], [[1, 2, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[0], [0], 是], [[0, 3], [0, 2], 是], [[0, 1, 3], [0, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 性質不同)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-open-map-contrast","seed":202610193084,"parameters":{"n":4,"m":4,"opens_x":[[],[0],[0,3],[0,1,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[0,3,1,2],"domain":"Fin_topological_map","operation":"continuity-open-map-contrast","semantic_template":"qf-ext19-continuity-open-map-contrast/{\"images\":[0,3,1,2],\"m\":4,\"n\":4,\"opens_x\":[[],[0],[0,3],[0,1,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0085","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-open-map-contrast；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[1],[1,3],[0,1,3],[0,1,2,3]],\"opens_y\":[[],[1],[1,3],[1,2,3],[0,1,2,3]],\"images\":[1,3,0,2]}。請依 [images,continuous,open_map,preimage_rows,image_rows,comparison] 欄序回答。","answer":{"kind":"expression","value":"([1, 3, 0, 2], 否, 否, [[[], [], 是], [[1], [0], 否], [[1, 3], [0, 1], 否], [[1, 2, 3], [0, 1, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[1], [3], 否], [[1, 3], [2, 3], 否], [[0, 1, 3], [1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 同值但責任不同)","explanation_zh":"第二批擴展核對=([1, 3, 0, 2], 否, 否, [[[], [], 是], [[1], [0], 否], [[1, 3], [0, 1], 否], [[1, 2, 3], [0, 1, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[1], [3], 否], [[1, 3], [2, 3], 否], [[0, 1, 3], [1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 同值但責任不同)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-open-map-contrast","seed":202610193085,"parameters":{"n":4,"m":4,"opens_x":[[],[1],[1,3],[0,1,3],[0,1,2,3]],"opens_y":[[],[1],[1,3],[1,2,3],[0,1,2,3]],"images":[1,3,0,2],"domain":"Fin_topological_map","operation":"continuity-open-map-contrast","semantic_template":"qf-ext19-continuity-open-map-contrast/{\"images\":[1,3,0,2],\"m\":4,\"n\":4,\"opens_x\":[[],[1],[1,3],[0,1,3],[0,1,2,3]],\"opens_y\":[[],[1],[1,3],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0086","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-open-map-contrast；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[2],[2,3],[0,2,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"images\":[2,3,0,1]}。請依 [images,continuous,open_map,preimage_rows,image_rows,comparison] 欄序回答。","answer":{"kind":"expression","value":"([2, 3, 0, 1], 否, 是, [[[], [], 是], [[0], [2], 是], [[1], [3], 否], [[0, 1], [2, 3], 是], [[2], [0], 否], [[0, 2], [0, 2], 否], [[1, 2], [0, 3], 否], [[0, 1, 2], [0, 2, 3], 是], [[3], [1], 否], [[0, 3], [1, 2], 否], [[1, 3], [1, 3], 否], [[0, 1, 3], [1, 2, 3], 否], [[2, 3], [0, 1], 否], [[0, 2, 3], [0, 1, 2], 否], [[1, 2, 3], [0, 1, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[2], [0], 是], [[2, 3], [0, 1], 是], [[0, 2, 3], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 性質不同)","explanation_zh":"第二批擴展核對=([2, 3, 0, 1], 否, 是, [[[], [], 是], [[0], [2], 是], [[1], [3], 否], [[0, 1], [2, 3], 是], [[2], [0], 否], [[0, 2], [0, 2], 否], [[1, 2], [0, 3], 否], [[0, 1, 2], [0, 2, 3], 是], [[3], [1], 否], [[0, 3], [1, 2], 否], [[1, 3], [1, 3], 否], [[0, 1, 3], [1, 2, 3], 否], [[2, 3], [0, 1], 否], [[0, 2, 3], [0, 1, 2], 否], [[1, 2, 3], [0, 1, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[2], [0], 是], [[2, 3], [0, 1], 是], [[0, 2, 3], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 性質不同)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-open-map-contrast","seed":202610193086,"parameters":{"n":4,"m":4,"opens_x":[[],[2],[2,3],[0,2,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[2,3,0,1],"domain":"Fin_topological_map","operation":"continuity-open-map-contrast","semantic_template":"qf-ext19-continuity-open-map-contrast/{\"images\":[2,3,0,1],\"m\":4,\"n\":4,\"opens_x\":[[],[2],[2,3],[0,2,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0087","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-open-map-contrast；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[3],[2,3],[0,2,3],[0,1,2,3]],\"opens_y\":[[],[3],[1,3],[0,1,3],[0,1,2,3]],\"images\":[3,2,0,1]}。請依 [images,continuous,open_map,preimage_rows,image_rows,comparison] 欄序回答。","answer":{"kind":"expression","value":"([3, 2, 0, 1], 否, 否, [[[], [], 是], [[3], [0], 否], [[1, 3], [0, 3], 否], [[0, 1, 3], [0, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[3], [1], 否], [[2, 3], [0, 1], 否], [[0, 2, 3], [0, 1, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 同值但責任不同)","explanation_zh":"第二批擴展核對=([3, 2, 0, 1], 否, 否, [[[], [], 是], [[3], [0], 否], [[1, 3], [0, 3], 否], [[0, 1, 3], [0, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[3], [1], 否], [[2, 3], [0, 1], 否], [[0, 2, 3], [0, 1, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 同值但責任不同)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-open-map-contrast","seed":202610193087,"parameters":{"n":4,"m":4,"opens_x":[[],[3],[2,3],[0,2,3],[0,1,2,3]],"opens_y":[[],[3],[1,3],[0,1,3],[0,1,2,3]],"images":[3,2,0,1],"domain":"Fin_topological_map","operation":"continuity-open-map-contrast","semantic_template":"qf-ext19-continuity-open-map-contrast/{\"images\":[3,2,0,1],\"m\":4,\"n\":4,\"opens_x\":[[],[3],[2,3],[0,2,3],[0,1,2,3]],\"opens_y\":[[],[3],[1,3],[0,1,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0088","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-open-map-contrast；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[0],[0,1],[0,1,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"images\":[0,1,3,2]}。請依 [images,continuous,open_map,preimage_rows,image_rows,comparison] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 3, 2], 否, 是, [[[], [], 是], [[0], [0], 是], [[1], [1], 否], [[0, 1], [0, 1], 是], [[2], [3], 否], [[0, 2], [0, 3], 否], [[1, 2], [1, 3], 否], [[0, 1, 2], [0, 1, 3], 是], [[3], [2], 否], [[0, 3], [0, 2], 否], [[1, 3], [1, 2], 否], [[0, 1, 3], [0, 1, 2], 否], [[2, 3], [2, 3], 否], [[0, 2, 3], [0, 2, 3], 否], [[1, 2, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[0], [0], 是], [[0, 1], [0, 1], 是], [[0, 1, 3], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 性質不同)","explanation_zh":"第二批擴展核對=([0, 1, 3, 2], 否, 是, [[[], [], 是], [[0], [0], 是], [[1], [1], 否], [[0, 1], [0, 1], 是], [[2], [3], 否], [[0, 2], [0, 3], 否], [[1, 2], [1, 3], 否], [[0, 1, 2], [0, 1, 3], 是], [[3], [2], 否], [[0, 3], [0, 2], 否], [[1, 3], [1, 2], 否], [[0, 1, 3], [0, 1, 2], 否], [[2, 3], [2, 3], 否], [[0, 2, 3], [0, 2, 3], 否], [[1, 2, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[0], [0], 是], [[0, 1], [0, 1], 是], [[0, 1, 3], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 性質不同)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-open-map-contrast","seed":202610193088,"parameters":{"n":4,"m":4,"opens_x":[[],[0],[0,1],[0,1,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[0,1,3,2],"domain":"Fin_topological_map","operation":"continuity-open-map-contrast","semantic_template":"qf-ext19-continuity-open-map-contrast/{\"images\":[0,1,3,2],\"m\":4,\"n\":4,\"opens_x\":[[],[0],[0,1],[0,1,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0089","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-open-map-contrast；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[1],[0,1],[0,1,3],[0,1,2,3]],\"opens_y\":[[],[1],[1,2],[1,2,3],[0,1,2,3]],\"images\":[1,0,3,2]}。請依 [images,continuous,open_map,preimage_rows,image_rows,comparison] 欄序回答。","answer":{"kind":"expression","value":"([1, 0, 3, 2], 否, 否, [[[], [], 是], [[1], [0], 否], [[1, 2], [0, 3], 否], [[1, 2, 3], [0, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[1], [0], 否], [[0, 1], [0, 1], 否], [[0, 1, 3], [0, 1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 同值但責任不同)","explanation_zh":"第二批擴展核對=([1, 0, 3, 2], 否, 否, [[[], [], 是], [[1], [0], 否], [[1, 2], [0, 3], 否], [[1, 2, 3], [0, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[1], [0], 否], [[0, 1], [0, 1], 否], [[0, 1, 3], [0, 1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 同值但責任不同)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-open-map-contrast","seed":202610193089,"parameters":{"n":4,"m":4,"opens_x":[[],[1],[0,1],[0,1,3],[0,1,2,3]],"opens_y":[[],[1],[1,2],[1,2,3],[0,1,2,3]],"images":[1,0,3,2],"domain":"Fin_topological_map","operation":"continuity-open-map-contrast","semantic_template":"qf-ext19-continuity-open-map-contrast/{\"images\":[1,0,3,2],\"m\":4,\"n\":4,\"opens_x\":[[],[1],[0,1],[0,1,3],[0,1,2,3]],\"opens_y\":[[],[1],[1,2],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0090","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-open-map-contrast；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[2],[0,2],[0,2,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"images\":[2,0,3,1]}。請依 [images,continuous,open_map,preimage_rows,image_rows,comparison] 欄序回答。","answer":{"kind":"expression","value":"([2, 0, 3, 1], 否, 是, [[[], [], 是], [[0], [1], 否], [[1], [3], 否], [[0, 1], [1, 3], 否], [[2], [0], 否], [[0, 2], [0, 1], 否], [[1, 2], [0, 3], 否], [[0, 1, 2], [0, 1, 3], 否], [[3], [2], 是], [[0, 3], [1, 2], 否], [[1, 3], [2, 3], 否], [[0, 1, 3], [1, 2, 3], 否], [[2, 3], [0, 2], 是], [[0, 2, 3], [0, 1, 2], 否], [[1, 2, 3], [0, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[2], [3], 是], [[0, 2], [2, 3], 是], [[0, 2, 3], [1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 性質不同)","explanation_zh":"第二批擴展核對=([2, 0, 3, 1], 否, 是, [[[], [], 是], [[0], [1], 否], [[1], [3], 否], [[0, 1], [1, 3], 否], [[2], [0], 否], [[0, 2], [0, 1], 否], [[1, 2], [0, 3], 否], [[0, 1, 2], [0, 1, 3], 否], [[3], [2], 是], [[0, 3], [1, 2], 否], [[1, 3], [2, 3], 否], [[0, 1, 3], [1, 2, 3], 否], [[2, 3], [0, 2], 是], [[0, 2, 3], [0, 1, 2], 否], [[1, 2, 3], [0, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[2], [3], 是], [[0, 2], [2, 3], 是], [[0, 2, 3], [1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 性質不同)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-open-map-contrast","seed":202610193090,"parameters":{"n":4,"m":4,"opens_x":[[],[2],[0,2],[0,2,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[2,0,3,1],"domain":"Fin_topological_map","operation":"continuity-open-map-contrast","semantic_template":"qf-ext19-continuity-open-map-contrast/{\"images\":[2,0,3,1],\"m\":4,\"n\":4,\"opens_x\":[[],[2],[0,2],[0,2,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0091","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-open-map-contrast；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[3],[0,3],[0,2,3],[0,1,2,3]],\"opens_y\":[[],[3],[0,3],[0,1,3],[0,1,2,3]],\"images\":[3,0,2,1]}。請依 [images,continuous,open_map,preimage_rows,image_rows,comparison] 欄序回答。","answer":{"kind":"expression","value":"([3, 0, 2, 1], 否, 否, [[[], [], 是], [[3], [0], 否], [[0, 3], [0, 1], 否], [[0, 1, 3], [0, 1, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[3], [1], 否], [[0, 3], [1, 3], 否], [[0, 2, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 同值但責任不同)","explanation_zh":"第二批擴展核對=([3, 0, 2, 1], 否, 否, [[[], [], 是], [[3], [0], 否], [[0, 3], [0, 1], 否], [[0, 1, 3], [0, 1, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[3], [1], 否], [[0, 3], [1, 3], 否], [[0, 2, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 同值但責任不同)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-open-map-contrast","seed":202610193091,"parameters":{"n":4,"m":4,"opens_x":[[],[3],[0,3],[0,2,3],[0,1,2,3]],"opens_y":[[],[3],[0,3],[0,1,3],[0,1,2,3]],"images":[3,0,2,1],"domain":"Fin_topological_map","operation":"continuity-open-map-contrast","semantic_template":"qf-ext19-continuity-open-map-contrast/{\"images\":[3,0,2,1],\"m\":4,\"n\":4,\"opens_x\":[[],[3],[0,3],[0,2,3],[0,1,2,3]],\"opens_y\":[[],[3],[0,3],[0,1,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0092","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-open-map-contrast；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[0],[0,2],[0,2,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"images\":[0,2,3,1]}。請依 [images,continuous,open_map,preimage_rows,image_rows,comparison] 欄序回答。","answer":{"kind":"expression","value":"([0, 2, 3, 1], 否, 是, [[[], [], 是], [[0], [0], 是], [[1], [3], 否], [[0, 1], [0, 3], 否], [[2], [1], 否], [[0, 2], [0, 1], 否], [[1, 2], [1, 3], 否], [[0, 1, 2], [0, 1, 3], 否], [[3], [2], 否], [[0, 3], [0, 2], 是], [[1, 3], [2, 3], 否], [[0, 1, 3], [0, 2, 3], 是], [[2, 3], [1, 2], 否], [[0, 2, 3], [0, 1, 2], 否], [[1, 2, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[0], [0], 是], [[0, 2], [0, 3], 是], [[0, 2, 3], [0, 1, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 性質不同)","explanation_zh":"第二批擴展核對=([0, 2, 3, 1], 否, 是, [[[], [], 是], [[0], [0], 是], [[1], [3], 否], [[0, 1], [0, 3], 否], [[2], [1], 否], [[0, 2], [0, 1], 否], [[1, 2], [1, 3], 否], [[0, 1, 2], [0, 1, 3], 否], [[3], [2], 否], [[0, 3], [0, 2], 是], [[1, 3], [2, 3], 否], [[0, 1, 3], [0, 2, 3], 是], [[2, 3], [1, 2], 否], [[0, 2, 3], [0, 1, 2], 否], [[1, 2, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[0], [0], 是], [[0, 2], [0, 3], 是], [[0, 2, 3], [0, 1, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 性質不同)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-open-map-contrast","seed":202610193092,"parameters":{"n":4,"m":4,"opens_x":[[],[0],[0,2],[0,2,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[0,2,3,1],"domain":"Fin_topological_map","operation":"continuity-open-map-contrast","semantic_template":"qf-ext19-continuity-open-map-contrast/{\"images\":[0,2,3,1],\"m\":4,\"n\":4,\"opens_x\":[[],[0],[0,2],[0,2,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0093","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-open-map-contrast；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[1],[1,2],[1,2,3],[0,1,2,3]],\"opens_y\":[[],[1],[0,1],[0,1,3],[0,1,2,3]],\"images\":[1,2,3,0]}。請依 [images,continuous,open_map,preimage_rows,image_rows,comparison] 欄序回答。","answer":{"kind":"expression","value":"([1, 2, 3, 0], 否, 否, [[[], [], 是], [[1], [0], 否], [[0, 1], [0, 3], 否], [[0, 1, 3], [0, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[1], [2], 否], [[1, 2], [2, 3], 否], [[1, 2, 3], [0, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 同值但責任不同)","explanation_zh":"第二批擴展核對=([1, 2, 3, 0], 否, 否, [[[], [], 是], [[1], [0], 否], [[0, 1], [0, 3], 否], [[0, 1, 3], [0, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[1], [2], 否], [[1, 2], [2, 3], 否], [[1, 2, 3], [0, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 同值但責任不同)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-open-map-contrast","seed":202610193093,"parameters":{"n":4,"m":4,"opens_x":[[],[1],[1,2],[1,2,3],[0,1,2,3]],"opens_y":[[],[1],[0,1],[0,1,3],[0,1,2,3]],"images":[1,2,3,0],"domain":"Fin_topological_map","operation":"continuity-open-map-contrast","semantic_template":"qf-ext19-continuity-open-map-contrast/{\"images\":[1,2,3,0],\"m\":4,\"n\":4,\"opens_x\":[[],[1],[1,2],[1,2,3],[0,1,2,3]],\"opens_y\":[[],[1],[0,1],[0,1,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0094","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-open-map-contrast；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[2],[1,2],[1,2,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"images\":[2,1,3,0]}。請依 [images,continuous,open_map,preimage_rows,image_rows,comparison] 欄序回答。","answer":{"kind":"expression","value":"([2, 1, 3, 0], 否, 是, [[[], [], 是], [[0], [3], 否], [[1], [1], 否], [[0, 1], [1, 3], 否], [[2], [0], 否], [[0, 2], [0, 3], 否], [[1, 2], [0, 1], 否], [[0, 1, 2], [0, 1, 3], 否], [[3], [2], 是], [[0, 3], [2, 3], 否], [[1, 3], [1, 2], 是], [[0, 1, 3], [1, 2, 3], 是], [[2, 3], [0, 2], 否], [[0, 2, 3], [0, 2, 3], 否], [[1, 2, 3], [0, 1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[2], [3], 是], [[1, 2], [1, 3], 是], [[1, 2, 3], [0, 1, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 性質不同)","explanation_zh":"第二批擴展核對=([2, 1, 3, 0], 否, 是, [[[], [], 是], [[0], [3], 否], [[1], [1], 否], [[0, 1], [1, 3], 否], [[2], [0], 否], [[0, 2], [0, 3], 否], [[1, 2], [0, 1], 否], [[0, 1, 2], [0, 1, 3], 否], [[3], [2], 是], [[0, 3], [2, 3], 否], [[1, 3], [1, 2], 是], [[0, 1, 3], [1, 2, 3], 是], [[2, 3], [0, 2], 否], [[0, 2, 3], [0, 2, 3], 否], [[1, 2, 3], [0, 1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[2], [3], 是], [[1, 2], [1, 3], 是], [[1, 2, 3], [0, 1, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 性質不同)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-open-map-contrast","seed":202610193094,"parameters":{"n":4,"m":4,"opens_x":[[],[2],[1,2],[1,2,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[2,1,3,0],"domain":"Fin_topological_map","operation":"continuity-open-map-contrast","semantic_template":"qf-ext19-continuity-open-map-contrast/{\"images\":[2,1,3,0],\"m\":4,\"n\":4,\"opens_x\":[[],[2],[1,2],[1,2,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0095","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-open-map-contrast；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[3],[1,3],[1,2,3],[0,1,2,3]],\"opens_y\":[[],[3],[2,3],[1,2,3],[0,1,2,3]],\"images\":[3,1,2,0]}。請依 [images,continuous,open_map,preimage_rows,image_rows,comparison] 欄序回答。","answer":{"kind":"expression","value":"([3, 1, 2, 0], 否, 否, [[[], [], 是], [[3], [0], 否], [[2, 3], [0, 2], 否], [[1, 2, 3], [0, 1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[3], [0], 否], [[1, 3], [0, 1], 否], [[1, 2, 3], [0, 1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 同值但責任不同)","explanation_zh":"第二批擴展核對=([3, 1, 2, 0], 否, 否, [[[], [], 是], [[3], [0], 否], [[2, 3], [0, 2], 否], [[1, 2, 3], [0, 1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[3], [0], 否], [[1, 3], [0, 1], 否], [[1, 2, 3], [0, 1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 同值但責任不同)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-open-map-contrast","seed":202610193095,"parameters":{"n":4,"m":4,"opens_x":[[],[3],[1,3],[1,2,3],[0,1,2,3]],"opens_y":[[],[3],[2,3],[1,2,3],[0,1,2,3]],"images":[3,1,2,0],"domain":"Fin_topological_map","operation":"continuity-open-map-contrast","semantic_template":"qf-ext19-continuity-open-map-contrast/{\"images\":[3,1,2,0],\"m\":4,\"n\":4,\"opens_x\":[[],[3],[1,3],[1,2,3],[0,1,2,3]],\"opens_y\":[[],[3],[2,3],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0096","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-open-map-contrast；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[0],[0,3],[0,2,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"images\":[0,3,2,1]}。請依 [images,continuous,open_map,preimage_rows,image_rows,comparison] 欄序回答。","answer":{"kind":"expression","value":"([0, 3, 2, 1], 否, 是, [[[], [], 是], [[0], [0], 是], [[1], [3], 否], [[0, 1], [0, 3], 是], [[2], [2], 否], [[0, 2], [0, 2], 否], [[1, 2], [2, 3], 否], [[0, 1, 2], [0, 2, 3], 是], [[3], [1], 否], [[0, 3], [0, 1], 否], [[1, 3], [1, 3], 否], [[0, 1, 3], [0, 1, 3], 否], [[2, 3], [1, 2], 否], [[0, 2, 3], [0, 1, 2], 否], [[1, 2, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[0], [0], 是], [[0, 3], [0, 1], 是], [[0, 2, 3], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 性質不同)","explanation_zh":"第二批擴展核對=([0, 3, 2, 1], 否, 是, [[[], [], 是], [[0], [0], 是], [[1], [3], 否], [[0, 1], [0, 3], 是], [[2], [2], 否], [[0, 2], [0, 2], 否], [[1, 2], [2, 3], 否], [[0, 1, 2], [0, 2, 3], 是], [[3], [1], 否], [[0, 3], [0, 1], 否], [[1, 3], [1, 3], 否], [[0, 1, 3], [0, 1, 3], 否], [[2, 3], [1, 2], 否], [[0, 2, 3], [0, 1, 2], 否], [[1, 2, 3], [1, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[0], [0], 是], [[0, 3], [0, 1], 是], [[0, 2, 3], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 性質不同)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-open-map-contrast","seed":202610193096,"parameters":{"n":4,"m":4,"opens_x":[[],[0],[0,3],[0,2,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[0,3,2,1],"domain":"Fin_topological_map","operation":"continuity-open-map-contrast","semantic_template":"qf-ext19-continuity-open-map-contrast/{\"images\":[0,3,2,1],\"m\":4,\"n\":4,\"opens_x\":[[],[0],[0,3],[0,2,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0097","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-open-map-contrast；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[1],[1,3],[1,2,3],[0,1,2,3]],\"opens_y\":[[],[1],[1,3],[0,1,3],[0,1,2,3]],\"images\":[1,3,2,0]}。請依 [images,continuous,open_map,preimage_rows,image_rows,comparison] 欄序回答。","answer":{"kind":"expression","value":"([1, 3, 2, 0], 否, 否, [[[], [], 是], [[1], [0], 否], [[1, 3], [0, 1], 否], [[0, 1, 3], [0, 1, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[1], [3], 否], [[1, 3], [0, 3], 否], [[1, 2, 3], [0, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 同值但責任不同)","explanation_zh":"第二批擴展核對=([1, 3, 2, 0], 否, 否, [[[], [], 是], [[1], [0], 否], [[1, 3], [0, 1], 否], [[0, 1, 3], [0, 1, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[1], [3], 否], [[1, 3], [0, 3], 否], [[1, 2, 3], [0, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 同值但責任不同)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-open-map-contrast","seed":202610193097,"parameters":{"n":4,"m":4,"opens_x":[[],[1],[1,3],[1,2,3],[0,1,2,3]],"opens_y":[[],[1],[1,3],[0,1,3],[0,1,2,3]],"images":[1,3,2,0],"domain":"Fin_topological_map","operation":"continuity-open-map-contrast","semantic_template":"qf-ext19-continuity-open-map-contrast/{\"images\":[1,3,2,0],\"m\":4,\"n\":4,\"opens_x\":[[],[1],[1,3],[1,2,3],[0,1,2,3]],\"opens_y\":[[],[1],[1,3],[0,1,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0098","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-open-map-contrast；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[2],[2,3],[1,2,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"images\":[2,3,1,0]}。請依 [images,continuous,open_map,preimage_rows,image_rows,comparison] 欄序回答。","answer":{"kind":"expression","value":"([2, 3, 1, 0], 否, 是, [[[], [], 是], [[0], [3], 否], [[1], [2], 是], [[0, 1], [2, 3], 是], [[2], [0], 否], [[0, 2], [0, 3], 否], [[1, 2], [0, 2], 否], [[0, 1, 2], [0, 2, 3], 否], [[3], [1], 否], [[0, 3], [1, 3], 否], [[1, 3], [1, 2], 否], [[0, 1, 3], [1, 2, 3], 是], [[2, 3], [0, 1], 否], [[0, 2, 3], [0, 1, 3], 否], [[1, 2, 3], [0, 1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[2], [1], 是], [[2, 3], [0, 1], 是], [[1, 2, 3], [0, 1, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 性質不同)","explanation_zh":"第二批擴展核對=([2, 3, 1, 0], 否, 是, [[[], [], 是], [[0], [3], 否], [[1], [2], 是], [[0, 1], [2, 3], 是], [[2], [0], 否], [[0, 2], [0, 3], 否], [[1, 2], [0, 2], 否], [[0, 1, 2], [0, 2, 3], 否], [[3], [1], 否], [[0, 3], [1, 3], 否], [[1, 3], [1, 2], 否], [[0, 1, 3], [1, 2, 3], 是], [[2, 3], [0, 1], 否], [[0, 2, 3], [0, 1, 3], 否], [[1, 2, 3], [0, 1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[2], [1], 是], [[2, 3], [0, 1], 是], [[1, 2, 3], [0, 1, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 性質不同)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-open-map-contrast","seed":202610193098,"parameters":{"n":4,"m":4,"opens_x":[[],[2],[2,3],[1,2,3],[0,1,2,3]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"images":[2,3,1,0],"domain":"Fin_topological_map","operation":"continuity-open-map-contrast","semantic_template":"qf-ext19-continuity-open-map-contrast/{\"images\":[2,3,1,0],\"m\":4,\"n\":4,\"opens_x\":[[],[2],[2,3],[1,2,3],[0,1,2,3]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0099","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-open-map-contrast；資料={\"n\":4,\"m\":4,\"opens_x\":[[],[3],[2,3],[1,2,3],[0,1,2,3]],\"opens_y\":[[],[3],[1,3],[1,2,3],[0,1,2,3]],\"images\":[3,2,1,0]}。請依 [images,continuous,open_map,preimage_rows,image_rows,comparison] 欄序回答。","answer":{"kind":"expression","value":"([3, 2, 1, 0], 否, 否, [[[], [], 是], [[3], [0], 否], [[1, 3], [0, 2], 否], [[1, 2, 3], [0, 1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[3], [0], 否], [[2, 3], [0, 1], 否], [[1, 2, 3], [0, 1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 同值但責任不同)","explanation_zh":"第二批擴展核對=([3, 2, 1, 0], 否, 否, [[[], [], 是], [[3], [0], 否], [[1, 3], [0, 2], 否], [[1, 2, 3], [0, 1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], [[[], [], 是], [[3], [0], 否], [[2, 3], [0, 1], 否], [[1, 2, 3], [0, 1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 同值但責任不同)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-open-map-contrast","seed":202610193099,"parameters":{"n":4,"m":4,"opens_x":[[],[3],[2,3],[1,2,3],[0,1,2,3]],"opens_y":[[],[3],[1,3],[1,2,3],[0,1,2,3]],"images":[3,2,1,0],"domain":"Fin_topological_map","operation":"continuity-open-map-contrast","semantic_template":"qf-ext19-continuity-open-map-contrast/{\"images\":[3,2,1,0],\"m\":4,\"n\":4,\"opens_x\":[[],[3],[2,3],[1,2,3],[0,1,2,3]],\"opens_y\":[[],[3],[1,3],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r03-topological-continuity-0100","batch_id":"batch-20261013-advance-20261019-r03-topological-continuity-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-continuity"],"title_zh":"有限拓撲連續性","stem_zh":"完整有限拓撲與總映射。操作=continuity-open-map-contrast；資料={\"n\":3,\"m\":3,\"opens_x\":[[],[0],[0,1],[0,1,2]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2]],\"images\":[0,1,2]}。請依 [images,continuous,open_map,preimage_rows,image_rows,comparison] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2], 否, 是, [[[], [], 是], [[0], [0], 是], [[1], [1], 否], [[0, 1], [0, 1], 是], [[2], [2], 否], [[0, 2], [0, 2], 否], [[1, 2], [1, 2], 否], [[0, 1, 2], [0, 1, 2], 是]], [[[], [], 是], [[0], [0], 是], [[0, 1], [0, 1], 是], [[0, 1, 2], [0, 1, 2], 是]], 性質不同)","explanation_zh":"第二批擴展核對=([0, 1, 2], 否, 是, [[[], [], 是], [[0], [0], 是], [[1], [1], 否], [[0, 1], [0, 1], 是], [[2], [2], 否], [[0, 2], [0, 2], 否], [[1, 2], [1, 2], 否], [[0, 1, 2], [0, 1, 2], 是]], [[[], [], 是], [[0], [0], 是], [[0, 1], [0, 1], 是], [[0, 1, 2], [0, 1, 2], 是]], 性質不同)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；逐一核對全部目標開集逆像；開映射與連續性分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲連續性"]},"variant":{"family_id":"qf-ext19-continuity-open-map-contrast","seed":202610193100,"parameters":{"n":3,"m":3,"opens_x":[[],[0],[0,1],[0,1,2]],"opens_y":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2]],"images":[0,1,2],"domain":"Fin_topological_map","operation":"continuity-open-map-contrast","semantic_template":"qf-ext19-continuity-open-map-contrast/{\"images\":[0,1,2],\"m\":3,\"n\":3,\"opens_x\":[[],[0],[0,1],[0,1,2]],\"opens_y\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}