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商拓撲基礎 · 脈衝 R05
本批已通過 Schema、去重、來源快照與獨立答案重算；仍未標記為人工審定。
本題庫已有對應的中英逐步詳解。原題的 candidate 與英文 ai_candidate 狀態保留；AI 覆核、有限計算與 Lean 形式證明分開標示。
batch-20261015-advance-20261117-r05-quotient-topology-foundations · 2026-10-15 · 100 題
欄序為來源綁定的呈現補充；原始 JSONL 與數學答案不變。
欄序與來源綁定資料
1. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-fibers；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1]],"y_points":["a","b"],"q_map":["a","a","b","b","b","b"]}。請依 [fibers, surjective, fiber_cover, certificate] 欄序回答。
查看答案與解釋
([[a, [0, 1]], [b, [2, 3, 4, 5]]], 是, 是, fibers_partition_X)
Wave6第十一層核對=([[a, [0, 1]], [b, [2, 3, 4, 5]]], 是, 是, fibers_partition_X)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-fibers · candidate
2. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-fibers；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,2]],"y_points":["a","b"],"q_map":["a","b","a","b","b","b"]}。請依 [fibers, surjective, fiber_cover, certificate] 欄序回答。
查看答案與解釋
([[a, [0, 2]], [b, [1, 3, 4, 5]]], 是, 是, fibers_partition_X)
Wave6第十一層核對=([[a, [0, 2]], [b, [1, 3, 4, 5]]], 是, 是, fibers_partition_X)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-fibers · candidate
3. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-fibers；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,2]],"y_points":["a","b"],"q_map":["a","a","a","b","b","b"]}。請依 [fibers, surjective, fiber_cover, certificate] 欄序回答。
查看答案與解釋
([[a, [0, 1, 2]], [b, [3, 4, 5]]], 是, 是, fibers_partition_X)
Wave6第十一層核對=([[a, [0, 1, 2]], [b, [3, 4, 5]]], 是, 是, fibers_partition_X)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-fibers · candidate
4. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-fibers；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,3]],"y_points":["a","b"],"q_map":["a","b","b","a","b","b"]}。請依 [fibers, surjective, fiber_cover, certificate] 欄序回答。
查看答案與解釋
([[a, [0, 3]], [b, [1, 2, 4, 5]]], 是, 是, fibers_partition_X)
Wave6第十一層核對=([[a, [0, 3]], [b, [1, 2, 4, 5]]], 是, 是, fibers_partition_X)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-fibers · candidate
5. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-fibers；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,3]],"y_points":["a","b"],"q_map":["a","a","b","a","b","b"]}。請依 [fibers, surjective, fiber_cover, certificate] 欄序回答。
查看答案與解釋
([[a, [0, 1, 3]], [b, [2, 4, 5]]], 是, 是, fibers_partition_X)
Wave6第十一層核對=([[a, [0, 1, 3]], [b, [2, 4, 5]]], 是, 是, fibers_partition_X)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-fibers · candidate
6. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-fibers；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,2,3]],"y_points":["a","b"],"q_map":["a","b","a","a","b","b"]}。請依 [fibers, surjective, fiber_cover, certificate] 欄序回答。
查看答案與解釋
([[a, [0, 2, 3]], [b, [1, 4, 5]]], 是, 是, fibers_partition_X)
Wave6第十一層核對=([[a, [0, 2, 3]], [b, [1, 4, 5]]], 是, 是, fibers_partition_X)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-fibers · candidate
7. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-fibers；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,2,3]],"y_points":["a","b"],"q_map":["a","a","a","a","b","b"]}。請依 [fibers, surjective, fiber_cover, certificate] 欄序回答。
查看答案與解釋
([[a, [0, 1, 2, 3]], [b, [4, 5]]], 是, 是, fibers_partition_X)
Wave6第十一層核對=([[a, [0, 1, 2, 3]], [b, [4, 5]]], 是, 是, fibers_partition_X)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-fibers · candidate
8. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-fibers；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,4]],"y_points":["a","b"],"q_map":["a","b","b","b","a","b"]}。請依 [fibers, surjective, fiber_cover, certificate] 欄序回答。
查看答案與解釋
([[a, [0, 4]], [b, [1, 2, 3, 5]]], 是, 是, fibers_partition_X)
Wave6第十一層核對=([[a, [0, 4]], [b, [1, 2, 3, 5]]], 是, 是, fibers_partition_X)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-fibers · candidate
9. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-fibers；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,4]],"y_points":["a","b"],"q_map":["a","a","b","b","a","b"]}。請依 [fibers, surjective, fiber_cover, certificate] 欄序回答。
查看答案與解釋
([[a, [0, 1, 4]], [b, [2, 3, 5]]], 是, 是, fibers_partition_X)
Wave6第十一層核對=([[a, [0, 1, 4]], [b, [2, 3, 5]]], 是, 是, fibers_partition_X)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-fibers · candidate
10. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-fibers；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,2,4]],"y_points":["a","b"],"q_map":["a","b","a","b","a","b"]}。請依 [fibers, surjective, fiber_cover, certificate] 欄序回答。
查看答案與解釋
([[a, [0, 2, 4]], [b, [1, 3, 5]]], 是, 是, fibers_partition_X)
Wave6第十一層核對=([[a, [0, 2, 4]], [b, [1, 3, 5]]], 是, 是, fibers_partition_X)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-fibers · candidate
11. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-fibers；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,2,4]],"y_points":["a","b"],"q_map":["a","a","a","b","a","b"]}。請依 [fibers, surjective, fiber_cover, certificate] 欄序回答。
查看答案與解釋
([[a, [0, 1, 2, 4]], [b, [3, 5]]], 是, 是, fibers_partition_X)
Wave6第十一層核對=([[a, [0, 1, 2, 4]], [b, [3, 5]]], 是, 是, fibers_partition_X)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-fibers · candidate
12. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-fibers；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,3,4]],"y_points":["a","b"],"q_map":["a","b","b","a","a","b"]}。請依 [fibers, surjective, fiber_cover, certificate] 欄序回答。
查看答案與解釋
([[a, [0, 3, 4]], [b, [1, 2, 5]]], 是, 是, fibers_partition_X)
Wave6第十一層核對=([[a, [0, 3, 4]], [b, [1, 2, 5]]], 是, 是, fibers_partition_X)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-fibers · candidate
13. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-fibers；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,3,4]],"y_points":["a","b"],"q_map":["a","a","b","a","a","b"]}。請依 [fibers, surjective, fiber_cover, certificate] 欄序回答。
查看答案與解釋
([[a, [0, 1, 3, 4]], [b, [2, 5]]], 是, 是, fibers_partition_X)
Wave6第十一層核對=([[a, [0, 1, 3, 4]], [b, [2, 5]]], 是, 是, fibers_partition_X)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-fibers · candidate
14. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-fibers；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,2,3,4]],"y_points":["a","b"],"q_map":["a","b","a","a","a","b"]}。請依 [fibers, surjective, fiber_cover, certificate] 欄序回答。
查看答案與解釋
([[a, [0, 2, 3, 4]], [b, [1, 5]]], 是, 是, fibers_partition_X)
Wave6第十一層核對=([[a, [0, 2, 3, 4]], [b, [1, 5]]], 是, 是, fibers_partition_X)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-fibers · candidate
15. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-fibers；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,2,3,4]],"y_points":["a","b"],"q_map":["a","a","a","a","a","b"]}。請依 [fibers, surjective, fiber_cover, certificate] 欄序回答。
查看答案與解釋
([[a, [0, 1, 2, 3, 4]], [b, [5]]], 是, 是, fibers_partition_X)
Wave6第十一層核對=([[a, [0, 1, 2, 3, 4]], [b, [5]]], 是, 是, fibers_partition_X)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-fibers · candidate
16. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-fibers；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,5]],"y_points":["a","b"],"q_map":["a","b","b","b","b","a"]}。請依 [fibers, surjective, fiber_cover, certificate] 欄序回答。
查看答案與解釋
([[a, [0, 5]], [b, [1, 2, 3, 4]]], 是, 是, fibers_partition_X)
Wave6第十一層核對=([[a, [0, 5]], [b, [1, 2, 3, 4]]], 是, 是, fibers_partition_X)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-fibers · candidate
17. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-fibers；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,5]],"y_points":["a","b"],"q_map":["a","a","b","b","b","a"]}。請依 [fibers, surjective, fiber_cover, certificate] 欄序回答。
查看答案與解釋
([[a, [0, 1, 5]], [b, [2, 3, 4]]], 是, 是, fibers_partition_X)
Wave6第十一層核對=([[a, [0, 1, 5]], [b, [2, 3, 4]]], 是, 是, fibers_partition_X)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-fibers · candidate
18. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-fibers；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,2,5]],"y_points":["a","b"],"q_map":["a","b","a","b","b","a"]}。請依 [fibers, surjective, fiber_cover, certificate] 欄序回答。
查看答案與解釋
([[a, [0, 2, 5]], [b, [1, 3, 4]]], 是, 是, fibers_partition_X)
Wave6第十一層核對=([[a, [0, 2, 5]], [b, [1, 3, 4]]], 是, 是, fibers_partition_X)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-fibers · candidate
19. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-fibers；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,2,5]],"y_points":["a","b"],"q_map":["a","a","a","b","b","a"]}。請依 [fibers, surjective, fiber_cover, certificate] 欄序回答。
查看答案與解釋
([[a, [0, 1, 2, 5]], [b, [3, 4]]], 是, 是, fibers_partition_X)
Wave6第十一層核對=([[a, [0, 1, 2, 5]], [b, [3, 4]]], 是, 是, fibers_partition_X)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-fibers · candidate
20. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-fibers；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,3,5]],"y_points":["a","b"],"q_map":["a","b","b","a","b","a"]}。請依 [fibers, surjective, fiber_cover, certificate] 欄序回答。
查看答案與解釋
([[a, [0, 3, 5]], [b, [1, 2, 4]]], 是, 是, fibers_partition_X)
Wave6第十一層核對=([[a, [0, 3, 5]], [b, [1, 2, 4]]], 是, 是, fibers_partition_X)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-fibers · candidate
21. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-fibers；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,3,5]],"y_points":["a","b"],"q_map":["a","a","b","a","b","a"]}。請依 [fibers, surjective, fiber_cover, certificate] 欄序回答。
查看答案與解釋
([[a, [0, 1, 3, 5]], [b, [2, 4]]], 是, 是, fibers_partition_X)
Wave6第十一層核對=([[a, [0, 1, 3, 5]], [b, [2, 4]]], 是, 是, fibers_partition_X)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-fibers · candidate
22. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-fibers；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,2,3,5]],"y_points":["a","b"],"q_map":["a","b","a","a","b","a"]}。請依 [fibers, surjective, fiber_cover, certificate] 欄序回答。
查看答案與解釋
([[a, [0, 2, 3, 5]], [b, [1, 4]]], 是, 是, fibers_partition_X)
Wave6第十一層核對=([[a, [0, 2, 3, 5]], [b, [1, 4]]], 是, 是, fibers_partition_X)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-fibers · candidate
23. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-fibers；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,2,3,5]],"y_points":["a","b"],"q_map":["a","a","a","a","b","a"]}。請依 [fibers, surjective, fiber_cover, certificate] 欄序回答。
查看答案與解釋
([[a, [0, 1, 2, 3, 5]], [b, [4]]], 是, 是, fibers_partition_X)
Wave6第十一層核對=([[a, [0, 1, 2, 3, 5]], [b, [4]]], 是, 是, fibers_partition_X)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-fibers · candidate
24. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-fibers；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,4,5]],"y_points":["a","b"],"q_map":["a","b","b","b","a","a"]}。請依 [fibers, surjective, fiber_cover, certificate] 欄序回答。
查看答案與解釋
([[a, [0, 4, 5]], [b, [1, 2, 3]]], 是, 是, fibers_partition_X)
Wave6第十一層核對=([[a, [0, 4, 5]], [b, [1, 2, 3]]], 是, 是, fibers_partition_X)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-fibers · candidate
25. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-fibers；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,4,5]],"y_points":["a","b"],"q_map":["a","a","b","b","a","a"]}。請依 [fibers, surjective, fiber_cover, certificate] 欄序回答。
查看答案與解釋
([[a, [0, 1, 4, 5]], [b, [2, 3]]], 是, 是, fibers_partition_X)
Wave6第十一層核對=([[a, [0, 1, 4, 5]], [b, [2, 3]]], 是, 是, fibers_partition_X)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-fibers · candidate
26. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-generation；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1]],"y_points":["a","b"],"q_map":["a","a","b","b","b","b"]}。請依 [fibers, final_topology, saturated_source_opens, open_count_correspondence, quotient_certificate, certificate] 欄序回答。
查看答案與解釋
([[a, [0, 1]], [b, [2, 3, 4, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 1]], 是, 是, U_open_iff_q_preimage_U_open)
Wave6第十一層核對=([[a, [0, 1]], [b, [2, 3, 4, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 1]], 是, 是, U_open_iff_q_preimage_U_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-topology-generation · candidate
27. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-generation；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,2]],"y_points":["a","b"],"q_map":["a","b","a","b","b","b"]}。請依 [fibers, final_topology, saturated_source_opens, open_count_correspondence, quotient_certificate, certificate] 欄序回答。
查看答案與解釋
([[a, [0, 2]], [b, [1, 3, 4, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 2]], 是, 是, U_open_iff_q_preimage_U_open)
Wave6第十一層核對=([[a, [0, 2]], [b, [1, 3, 4, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 2]], 是, 是, U_open_iff_q_preimage_U_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-topology-generation · candidate
28. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-generation；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,2]],"y_points":["a","b"],"q_map":["a","a","a","b","b","b"]}。請依 [fibers, final_topology, saturated_source_opens, open_count_correspondence, quotient_certificate, certificate] 欄序回答。
查看答案與解釋
([[a, [0, 1, 2]], [b, [3, 4, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 1, 2]], 是, 是, U_open_iff_q_preimage_U_open)
Wave6第十一層核對=([[a, [0, 1, 2]], [b, [3, 4, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 1, 2]], 是, 是, U_open_iff_q_preimage_U_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-topology-generation · candidate
29. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-generation；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,3]],"y_points":["a","b"],"q_map":["a","b","b","a","b","b"]}。請依 [fibers, final_topology, saturated_source_opens, open_count_correspondence, quotient_certificate, certificate] 欄序回答。
查看答案與解釋
([[a, [0, 3]], [b, [1, 2, 4, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 3]], 是, 是, U_open_iff_q_preimage_U_open)
Wave6第十一層核對=([[a, [0, 3]], [b, [1, 2, 4, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 3]], 是, 是, U_open_iff_q_preimage_U_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-topology-generation · candidate
30. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-generation；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,3]],"y_points":["a","b"],"q_map":["a","a","b","a","b","b"]}。請依 [fibers, final_topology, saturated_source_opens, open_count_correspondence, quotient_certificate, certificate] 欄序回答。
查看答案與解釋
([[a, [0, 1, 3]], [b, [2, 4, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 1, 3]], 是, 是, U_open_iff_q_preimage_U_open)
Wave6第十一層核對=([[a, [0, 1, 3]], [b, [2, 4, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 1, 3]], 是, 是, U_open_iff_q_preimage_U_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-topology-generation · candidate
31. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-generation；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,2,3]],"y_points":["a","b"],"q_map":["a","b","a","a","b","b"]}。請依 [fibers, final_topology, saturated_source_opens, open_count_correspondence, quotient_certificate, certificate] 欄序回答。
查看答案與解釋
([[a, [0, 2, 3]], [b, [1, 4, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 2, 3]], 是, 是, U_open_iff_q_preimage_U_open)
Wave6第十一層核對=([[a, [0, 2, 3]], [b, [1, 4, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 2, 3]], 是, 是, U_open_iff_q_preimage_U_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-topology-generation · candidate
32. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-generation；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,2,3]],"y_points":["a","b"],"q_map":["a","a","a","a","b","b"]}。請依 [fibers, final_topology, saturated_source_opens, open_count_correspondence, quotient_certificate, certificate] 欄序回答。
查看答案與解釋
([[a, [0, 1, 2, 3]], [b, [4, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 1, 2, 3]], 是, 是, U_open_iff_q_preimage_U_open)
Wave6第十一層核對=([[a, [0, 1, 2, 3]], [b, [4, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 1, 2, 3]], 是, 是, U_open_iff_q_preimage_U_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-topology-generation · candidate
33. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-generation；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,4]],"y_points":["a","b"],"q_map":["a","b","b","b","a","b"]}。請依 [fibers, final_topology, saturated_source_opens, open_count_correspondence, quotient_certificate, certificate] 欄序回答。
查看答案與解釋
([[a, [0, 4]], [b, [1, 2, 3, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 4]], 是, 是, U_open_iff_q_preimage_U_open)
Wave6第十一層核對=([[a, [0, 4]], [b, [1, 2, 3, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 4]], 是, 是, U_open_iff_q_preimage_U_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-topology-generation · candidate
34. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-generation；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,4]],"y_points":["a","b"],"q_map":["a","a","b","b","a","b"]}。請依 [fibers, final_topology, saturated_source_opens, open_count_correspondence, quotient_certificate, certificate] 欄序回答。
查看答案與解釋
([[a, [0, 1, 4]], [b, [2, 3, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 1, 4]], 是, 是, U_open_iff_q_preimage_U_open)
Wave6第十一層核對=([[a, [0, 1, 4]], [b, [2, 3, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 1, 4]], 是, 是, U_open_iff_q_preimage_U_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-topology-generation · candidate
35. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-generation；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,2,4]],"y_points":["a","b"],"q_map":["a","b","a","b","a","b"]}。請依 [fibers, final_topology, saturated_source_opens, open_count_correspondence, quotient_certificate, certificate] 欄序回答。
查看答案與解釋
([[a, [0, 2, 4]], [b, [1, 3, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 2, 4]], 是, 是, U_open_iff_q_preimage_U_open)
Wave6第十一層核對=([[a, [0, 2, 4]], [b, [1, 3, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 2, 4]], 是, 是, U_open_iff_q_preimage_U_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-topology-generation · candidate
36. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-generation；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,2,4]],"y_points":["a","b"],"q_map":["a","a","a","b","a","b"]}。請依 [fibers, final_topology, saturated_source_opens, open_count_correspondence, quotient_certificate, certificate] 欄序回答。
查看答案與解釋
([[a, [0, 1, 2, 4]], [b, [3, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 1, 2, 4]], 是, 是, U_open_iff_q_preimage_U_open)
Wave6第十一層核對=([[a, [0, 1, 2, 4]], [b, [3, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 1, 2, 4]], 是, 是, U_open_iff_q_preimage_U_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-topology-generation · candidate
37. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-generation；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,3,4]],"y_points":["a","b"],"q_map":["a","b","b","a","a","b"]}。請依 [fibers, final_topology, saturated_source_opens, open_count_correspondence, quotient_certificate, certificate] 欄序回答。
查看答案與解釋
([[a, [0, 3, 4]], [b, [1, 2, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 3, 4]], 是, 是, U_open_iff_q_preimage_U_open)
Wave6第十一層核對=([[a, [0, 3, 4]], [b, [1, 2, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 3, 4]], 是, 是, U_open_iff_q_preimage_U_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-topology-generation · candidate
38. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-generation；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,3,4]],"y_points":["a","b"],"q_map":["a","a","b","a","a","b"]}。請依 [fibers, final_topology, saturated_source_opens, open_count_correspondence, quotient_certificate, certificate] 欄序回答。
查看答案與解釋
([[a, [0, 1, 3, 4]], [b, [2, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 1, 3, 4]], 是, 是, U_open_iff_q_preimage_U_open)
Wave6第十一層核對=([[a, [0, 1, 3, 4]], [b, [2, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 1, 3, 4]], 是, 是, U_open_iff_q_preimage_U_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-topology-generation · candidate
39. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-generation；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,2,3,4]],"y_points":["a","b"],"q_map":["a","b","a","a","a","b"]}。請依 [fibers, final_topology, saturated_source_opens, open_count_correspondence, quotient_certificate, certificate] 欄序回答。
查看答案與解釋
([[a, [0, 2, 3, 4]], [b, [1, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 2, 3, 4]], 是, 是, U_open_iff_q_preimage_U_open)
Wave6第十一層核對=([[a, [0, 2, 3, 4]], [b, [1, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 2, 3, 4]], 是, 是, U_open_iff_q_preimage_U_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-topology-generation · candidate
40. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-generation；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,2,3,4]],"y_points":["a","b"],"q_map":["a","a","a","a","a","b"]}。請依 [fibers, final_topology, saturated_source_opens, open_count_correspondence, quotient_certificate, certificate] 欄序回答。
查看答案與解釋
([[a, [0, 1, 2, 3, 4]], [b, [5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4]], 是, 是, U_open_iff_q_preimage_U_open)
Wave6第十一層核對=([[a, [0, 1, 2, 3, 4]], [b, [5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4]], 是, 是, U_open_iff_q_preimage_U_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-topology-generation · candidate
41. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-generation；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,5]],"y_points":["a","b"],"q_map":["a","b","b","b","b","a"]}。請依 [fibers, final_topology, saturated_source_opens, open_count_correspondence, quotient_certificate, certificate] 欄序回答。
查看答案與解釋
([[a, [0, 5]], [b, [1, 2, 3, 4]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 5]], 是, 是, U_open_iff_q_preimage_U_open)
Wave6第十一層核對=([[a, [0, 5]], [b, [1, 2, 3, 4]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 5]], 是, 是, U_open_iff_q_preimage_U_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-topology-generation · candidate
42. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-generation；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,5]],"y_points":["a","b"],"q_map":["a","a","b","b","b","a"]}。請依 [fibers, final_topology, saturated_source_opens, open_count_correspondence, quotient_certificate, certificate] 欄序回答。
查看答案與解釋
([[a, [0, 1, 5]], [b, [2, 3, 4]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 1, 5]], 是, 是, U_open_iff_q_preimage_U_open)
Wave6第十一層核對=([[a, [0, 1, 5]], [b, [2, 3, 4]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 1, 5]], 是, 是, U_open_iff_q_preimage_U_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-topology-generation · candidate
43. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-generation；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,2,5]],"y_points":["a","b"],"q_map":["a","b","a","b","b","a"]}。請依 [fibers, final_topology, saturated_source_opens, open_count_correspondence, quotient_certificate, certificate] 欄序回答。
查看答案與解釋
([[a, [0, 2, 5]], [b, [1, 3, 4]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 2, 5]], 是, 是, U_open_iff_q_preimage_U_open)
Wave6第十一層核對=([[a, [0, 2, 5]], [b, [1, 3, 4]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 2, 5]], 是, 是, U_open_iff_q_preimage_U_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-topology-generation · candidate
44. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-generation；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,2,5]],"y_points":["a","b"],"q_map":["a","a","a","b","b","a"]}。請依 [fibers, final_topology, saturated_source_opens, open_count_correspondence, quotient_certificate, certificate] 欄序回答。
查看答案與解釋
([[a, [0, 1, 2, 5]], [b, [3, 4]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 1, 2, 5]], 是, 是, U_open_iff_q_preimage_U_open)
Wave6第十一層核對=([[a, [0, 1, 2, 5]], [b, [3, 4]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 1, 2, 5]], 是, 是, U_open_iff_q_preimage_U_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-topology-generation · candidate
45. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-generation；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,3,5]],"y_points":["a","b"],"q_map":["a","b","b","a","b","a"]}。請依 [fibers, final_topology, saturated_source_opens, open_count_correspondence, quotient_certificate, certificate] 欄序回答。
查看答案與解釋
([[a, [0, 3, 5]], [b, [1, 2, 4]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 3, 5]], 是, 是, U_open_iff_q_preimage_U_open)
Wave6第十一層核對=([[a, [0, 3, 5]], [b, [1, 2, 4]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 3, 5]], 是, 是, U_open_iff_q_preimage_U_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-topology-generation · candidate
46. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-generation；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,3,5]],"y_points":["a","b"],"q_map":["a","a","b","a","b","a"]}。請依 [fibers, final_topology, saturated_source_opens, open_count_correspondence, quotient_certificate, certificate] 欄序回答。
查看答案與解釋
([[a, [0, 1, 3, 5]], [b, [2, 4]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 1, 3, 5]], 是, 是, U_open_iff_q_preimage_U_open)
Wave6第十一層核對=([[a, [0, 1, 3, 5]], [b, [2, 4]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 1, 3, 5]], 是, 是, U_open_iff_q_preimage_U_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-topology-generation · candidate
47. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-generation；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,2,3,5]],"y_points":["a","b"],"q_map":["a","b","a","a","b","a"]}。請依 [fibers, final_topology, saturated_source_opens, open_count_correspondence, quotient_certificate, certificate] 欄序回答。
查看答案與解釋
([[a, [0, 2, 3, 5]], [b, [1, 4]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 2, 3, 5]], 是, 是, U_open_iff_q_preimage_U_open)
Wave6第十一層核對=([[a, [0, 2, 3, 5]], [b, [1, 4]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 2, 3, 5]], 是, 是, U_open_iff_q_preimage_U_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-topology-generation · candidate
48. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-generation；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,2,3,5]],"y_points":["a","b"],"q_map":["a","a","a","a","b","a"]}。請依 [fibers, final_topology, saturated_source_opens, open_count_correspondence, quotient_certificate, certificate] 欄序回答。
查看答案與解釋
([[a, [0, 1, 2, 3, 5]], [b, [4]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 5]], 是, 是, U_open_iff_q_preimage_U_open)
Wave6第十一層核對=([[a, [0, 1, 2, 3, 5]], [b, [4]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 5]], 是, 是, U_open_iff_q_preimage_U_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-topology-generation · candidate
49. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-generation；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,4,5]],"y_points":["a","b"],"q_map":["a","b","b","b","a","a"]}。請依 [fibers, final_topology, saturated_source_opens, open_count_correspondence, quotient_certificate, certificate] 欄序回答。
查看答案與解釋
([[a, [0, 4, 5]], [b, [1, 2, 3]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 4, 5]], 是, 是, U_open_iff_q_preimage_U_open)
Wave6第十一層核對=([[a, [0, 4, 5]], [b, [1, 2, 3]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 4, 5]], 是, 是, U_open_iff_q_preimage_U_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-topology-generation · candidate
50. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-generation；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,4,5]],"y_points":["a","b"],"q_map":["a","a","b","b","a","a"]}。請依 [fibers, final_topology, saturated_source_opens, open_count_correspondence, quotient_certificate, certificate] 欄序回答。
查看答案與解釋
([[a, [0, 1, 4, 5]], [b, [2, 3]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 1, 4, 5]], 是, 是, U_open_iff_q_preimage_U_open)
Wave6第十一層核對=([[a, [0, 1, 4, 5]], [b, [2, 3]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 1, 4, 5]], 是, 是, U_open_iff_q_preimage_U_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-topology-generation · candidate
51. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-final-continuity；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1]],"y_points":["a","b"],"q_map":["a","a","b","b","b","b"],"z_points":[0,1],"z_topology":[[],[1],[0,1]],"h_map":[0,1]}。請依 [h_continuous, composite_continuous, criterion_equivalence, h_rows, composite_rows, certificate] 欄序回答。
h與h∘q可同為不連續而criterion_equivalence為是；此等價需本節已認證的surjection與final topology。
查看答案與解釋
(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 0], [2, 1], [3, 1], [4, 1], [5, 1]], quotient_final_property_for_surjective_q)
Wave6第十一層核對=(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 0], [2, 1], [3, 1], [4, 1], [5, 1]], quotient_final_property_for_surjective_q)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-final-continuity · candidate
52. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-final-continuity；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,2]],"y_points":["a","b"],"q_map":["a","b","a","b","b","b"],"z_points":[0,1],"z_topology":[[],[1],[0,1]],"h_map":[0,1]}。請依 [h_continuous, composite_continuous, criterion_equivalence, h_rows, composite_rows, certificate] 欄序回答。
h與h∘q可同為不連續而criterion_equivalence為是；此等價需本節已認證的surjection與final topology。
查看答案與解釋
(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 0], [3, 1], [4, 1], [5, 1]], quotient_final_property_for_surjective_q)
Wave6第十一層核對=(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 0], [3, 1], [4, 1], [5, 1]], quotient_final_property_for_surjective_q)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-final-continuity · candidate
53. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-final-continuity；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,2]],"y_points":["a","b"],"q_map":["a","a","a","b","b","b"],"z_points":[0,1],"z_topology":[[],[1],[0,1]],"h_map":[0,1]}。請依 [h_continuous, composite_continuous, criterion_equivalence, h_rows, composite_rows, certificate] 欄序回答。
h與h∘q可同為不連續而criterion_equivalence為是；此等價需本節已認證的surjection與final topology。
查看答案與解釋
(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 0], [2, 0], [3, 1], [4, 1], [5, 1]], quotient_final_property_for_surjective_q)
Wave6第十一層核對=(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 0], [2, 0], [3, 1], [4, 1], [5, 1]], quotient_final_property_for_surjective_q)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-final-continuity · candidate
54. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-final-continuity；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,3]],"y_points":["a","b"],"q_map":["a","b","b","a","b","b"],"z_points":[0,1],"z_topology":[[],[1],[0,1]],"h_map":[0,1]}。請依 [h_continuous, composite_continuous, criterion_equivalence, h_rows, composite_rows, certificate] 欄序回答。
h與h∘q可同為不連續而criterion_equivalence為是；此等價需本節已認證的surjection與final topology。
查看答案與解釋
(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 1], [3, 0], [4, 1], [5, 1]], quotient_final_property_for_surjective_q)
Wave6第十一層核對=(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 1], [3, 0], [4, 1], [5, 1]], quotient_final_property_for_surjective_q)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-final-continuity · candidate
55. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-final-continuity；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,3]],"y_points":["a","b"],"q_map":["a","a","b","a","b","b"],"z_points":[0,1],"z_topology":[[],[1],[0,1]],"h_map":[0,1]}。請依 [h_continuous, composite_continuous, criterion_equivalence, h_rows, composite_rows, certificate] 欄序回答。
h與h∘q可同為不連續而criterion_equivalence為是；此等價需本節已認證的surjection與final topology。
查看答案與解釋
(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 0], [2, 1], [3, 0], [4, 1], [5, 1]], quotient_final_property_for_surjective_q)
Wave6第十一層核對=(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 0], [2, 1], [3, 0], [4, 1], [5, 1]], quotient_final_property_for_surjective_q)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-final-continuity · candidate
56. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-final-continuity；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,2,3]],"y_points":["a","b"],"q_map":["a","b","a","a","b","b"],"z_points":[0,1],"z_topology":[[],[1],[0,1]],"h_map":[0,1]}。請依 [h_continuous, composite_continuous, criterion_equivalence, h_rows, composite_rows, certificate] 欄序回答。
h與h∘q可同為不連續而criterion_equivalence為是；此等價需本節已認證的surjection與final topology。
查看答案與解釋
(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 0], [3, 0], [4, 1], [5, 1]], quotient_final_property_for_surjective_q)
Wave6第十一層核對=(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 0], [3, 0], [4, 1], [5, 1]], quotient_final_property_for_surjective_q)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-final-continuity · candidate
57. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-final-continuity；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,2,3]],"y_points":["a","b"],"q_map":["a","a","a","a","b","b"],"z_points":[0,1],"z_topology":[[],[1],[0,1]],"h_map":[0,1]}。請依 [h_continuous, composite_continuous, criterion_equivalence, h_rows, composite_rows, certificate] 欄序回答。
h與h∘q可同為不連續而criterion_equivalence為是；此等價需本節已認證的surjection與final topology。
查看答案與解釋
(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 0], [2, 0], [3, 0], [4, 1], [5, 1]], quotient_final_property_for_surjective_q)
Wave6第十一層核對=(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 0], [2, 0], [3, 0], [4, 1], [5, 1]], quotient_final_property_for_surjective_q)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-final-continuity · candidate
58. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-final-continuity；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,4]],"y_points":["a","b"],"q_map":["a","b","b","b","a","b"],"z_points":[0,1],"z_topology":[[],[1],[0,1]],"h_map":[0,1]}。請依 [h_continuous, composite_continuous, criterion_equivalence, h_rows, composite_rows, certificate] 欄序回答。
h與h∘q可同為不連續而criterion_equivalence為是；此等價需本節已認證的surjection與final topology。
查看答案與解釋
(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 1], [3, 1], [4, 0], [5, 1]], quotient_final_property_for_surjective_q)
Wave6第十一層核對=(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 1], [3, 1], [4, 0], [5, 1]], quotient_final_property_for_surjective_q)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-final-continuity · candidate
59. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-final-continuity；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,4]],"y_points":["a","b"],"q_map":["a","a","b","b","a","b"],"z_points":[0,1],"z_topology":[[],[1],[0,1]],"h_map":[0,1]}。請依 [h_continuous, composite_continuous, criterion_equivalence, h_rows, composite_rows, certificate] 欄序回答。
h與h∘q可同為不連續而criterion_equivalence為是；此等價需本節已認證的surjection與final topology。
查看答案與解釋
(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 0], [2, 1], [3, 1], [4, 0], [5, 1]], quotient_final_property_for_surjective_q)
Wave6第十一層核對=(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 0], [2, 1], [3, 1], [4, 0], [5, 1]], quotient_final_property_for_surjective_q)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-final-continuity · candidate
60. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-final-continuity；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,2,4]],"y_points":["a","b"],"q_map":["a","b","a","b","a","b"],"z_points":[0,1],"z_topology":[[],[1],[0,1]],"h_map":[0,1]}。請依 [h_continuous, composite_continuous, criterion_equivalence, h_rows, composite_rows, certificate] 欄序回答。
h與h∘q可同為不連續而criterion_equivalence為是；此等價需本節已認證的surjection與final topology。
查看答案與解釋
(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 0], [3, 1], [4, 0], [5, 1]], quotient_final_property_for_surjective_q)
Wave6第十一層核對=(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 0], [3, 1], [4, 0], [5, 1]], quotient_final_property_for_surjective_q)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-final-continuity · candidate
61. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-final-continuity；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,2,4]],"y_points":["a","b"],"q_map":["a","a","a","b","a","b"],"z_points":[0,1],"z_topology":[[],[1],[0,1]],"h_map":[0,1]}。請依 [h_continuous, composite_continuous, criterion_equivalence, h_rows, composite_rows, certificate] 欄序回答。
h與h∘q可同為不連續而criterion_equivalence為是；此等價需本節已認證的surjection與final topology。
查看答案與解釋
(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 0], [2, 0], [3, 1], [4, 0], [5, 1]], quotient_final_property_for_surjective_q)
Wave6第十一層核對=(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 0], [2, 0], [3, 1], [4, 0], [5, 1]], quotient_final_property_for_surjective_q)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-final-continuity · candidate
62. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-final-continuity；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,3,4]],"y_points":["a","b"],"q_map":["a","b","b","a","a","b"],"z_points":[0,1],"z_topology":[[],[1],[0,1]],"h_map":[0,1]}。請依 [h_continuous, composite_continuous, criterion_equivalence, h_rows, composite_rows, certificate] 欄序回答。
h與h∘q可同為不連續而criterion_equivalence為是；此等價需本節已認證的surjection與final topology。
查看答案與解釋
(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 1], [3, 0], [4, 0], [5, 1]], quotient_final_property_for_surjective_q)
Wave6第十一層核對=(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 1], [3, 0], [4, 0], [5, 1]], quotient_final_property_for_surjective_q)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-final-continuity · candidate
63. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-final-continuity；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,3,4]],"y_points":["a","b"],"q_map":["a","a","b","a","a","b"],"z_points":[0,1],"z_topology":[[],[1],[0,1]],"h_map":[0,1]}。請依 [h_continuous, composite_continuous, criterion_equivalence, h_rows, composite_rows, certificate] 欄序回答。
h與h∘q可同為不連續而criterion_equivalence為是；此等價需本節已認證的surjection與final topology。
查看答案與解釋
(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 0], [2, 1], [3, 0], [4, 0], [5, 1]], quotient_final_property_for_surjective_q)
Wave6第十一層核對=(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 0], [2, 1], [3, 0], [4, 0], [5, 1]], quotient_final_property_for_surjective_q)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-final-continuity · candidate
64. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-final-continuity；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,2,3,4]],"y_points":["a","b"],"q_map":["a","b","a","a","a","b"],"z_points":[0,1],"z_topology":[[],[1],[0,1]],"h_map":[0,1]}。請依 [h_continuous, composite_continuous, criterion_equivalence, h_rows, composite_rows, certificate] 欄序回答。
h與h∘q可同為不連續而criterion_equivalence為是；此等價需本節已認證的surjection與final topology。
查看答案與解釋
(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 0], [3, 0], [4, 0], [5, 1]], quotient_final_property_for_surjective_q)
Wave6第十一層核對=(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 0], [3, 0], [4, 0], [5, 1]], quotient_final_property_for_surjective_q)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-final-continuity · candidate
65. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-final-continuity；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,2,3,4]],"y_points":["a","b"],"q_map":["a","a","a","a","a","b"],"z_points":[0,1],"z_topology":[[],[1],[0,1]],"h_map":[0,1]}。請依 [h_continuous, composite_continuous, criterion_equivalence, h_rows, composite_rows, certificate] 欄序回答。
h與h∘q可同為不連續而criterion_equivalence為是；此等價需本節已認證的surjection與final topology。
查看答案與解釋
(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 0], [2, 0], [3, 0], [4, 0], [5, 1]], quotient_final_property_for_surjective_q)
Wave6第十一層核對=(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 0], [2, 0], [3, 0], [4, 0], [5, 1]], quotient_final_property_for_surjective_q)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-final-continuity · candidate
66. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-final-continuity；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,5]],"y_points":["a","b"],"q_map":["a","b","b","b","b","a"],"z_points":[0,1],"z_topology":[[],[1],[0,1]],"h_map":[0,1]}。請依 [h_continuous, composite_continuous, criterion_equivalence, h_rows, composite_rows, certificate] 欄序回答。
h與h∘q可同為不連續而criterion_equivalence為是；此等價需本節已認證的surjection與final topology。
查看答案與解釋
(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 1], [3, 1], [4, 1], [5, 0]], quotient_final_property_for_surjective_q)
Wave6第十一層核對=(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 1], [3, 1], [4, 1], [5, 0]], quotient_final_property_for_surjective_q)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-final-continuity · candidate
67. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-final-continuity；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,5]],"y_points":["a","b"],"q_map":["a","a","b","b","b","a"],"z_points":[0,1],"z_topology":[[],[1],[0,1]],"h_map":[0,1]}。請依 [h_continuous, composite_continuous, criterion_equivalence, h_rows, composite_rows, certificate] 欄序回答。
h與h∘q可同為不連續而criterion_equivalence為是；此等價需本節已認證的surjection與final topology。
查看答案與解釋
(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 0], [2, 1], [3, 1], [4, 1], [5, 0]], quotient_final_property_for_surjective_q)
Wave6第十一層核對=(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 0], [2, 1], [3, 1], [4, 1], [5, 0]], quotient_final_property_for_surjective_q)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-final-continuity · candidate
68. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-final-continuity；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,2,5]],"y_points":["a","b"],"q_map":["a","b","a","b","b","a"],"z_points":[0,1],"z_topology":[[],[1],[0,1]],"h_map":[0,1]}。請依 [h_continuous, composite_continuous, criterion_equivalence, h_rows, composite_rows, certificate] 欄序回答。
h與h∘q可同為不連續而criterion_equivalence為是；此等價需本節已認證的surjection與final topology。
查看答案與解釋
(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 0], [3, 1], [4, 1], [5, 0]], quotient_final_property_for_surjective_q)
Wave6第十一層核對=(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 0], [3, 1], [4, 1], [5, 0]], quotient_final_property_for_surjective_q)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-final-continuity · candidate
69. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-final-continuity；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,2,5]],"y_points":["a","b"],"q_map":["a","a","a","b","b","a"],"z_points":[0,1],"z_topology":[[],[1],[0,1]],"h_map":[0,1]}。請依 [h_continuous, composite_continuous, criterion_equivalence, h_rows, composite_rows, certificate] 欄序回答。
h與h∘q可同為不連續而criterion_equivalence為是；此等價需本節已認證的surjection與final topology。
查看答案與解釋
(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 0], [2, 0], [3, 1], [4, 1], [5, 0]], quotient_final_property_for_surjective_q)
Wave6第十一層核對=(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 0], [2, 0], [3, 1], [4, 1], [5, 0]], quotient_final_property_for_surjective_q)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-final-continuity · candidate
70. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-final-continuity；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,3,5]],"y_points":["a","b"],"q_map":["a","b","b","a","b","a"],"z_points":[0,1],"z_topology":[[],[1],[0,1]],"h_map":[0,1]}。請依 [h_continuous, composite_continuous, criterion_equivalence, h_rows, composite_rows, certificate] 欄序回答。
h與h∘q可同為不連續而criterion_equivalence為是；此等價需本節已認證的surjection與final topology。
查看答案與解釋
(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 1], [3, 0], [4, 1], [5, 0]], quotient_final_property_for_surjective_q)
Wave6第十一層核對=(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 1], [3, 0], [4, 1], [5, 0]], quotient_final_property_for_surjective_q)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-final-continuity · candidate
71. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-final-continuity；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,3,5]],"y_points":["a","b"],"q_map":["a","a","b","a","b","a"],"z_points":[0,1],"z_topology":[[],[1],[0,1]],"h_map":[0,1]}。請依 [h_continuous, composite_continuous, criterion_equivalence, h_rows, composite_rows, certificate] 欄序回答。
h與h∘q可同為不連續而criterion_equivalence為是；此等價需本節已認證的surjection與final topology。
查看答案與解釋
(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 0], [2, 1], [3, 0], [4, 1], [5, 0]], quotient_final_property_for_surjective_q)
Wave6第十一層核對=(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 0], [2, 1], [3, 0], [4, 1], [5, 0]], quotient_final_property_for_surjective_q)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-final-continuity · candidate
72. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-final-continuity；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,2,3,5]],"y_points":["a","b"],"q_map":["a","b","a","a","b","a"],"z_points":[0,1],"z_topology":[[],[1],[0,1]],"h_map":[0,1]}。請依 [h_continuous, composite_continuous, criterion_equivalence, h_rows, composite_rows, certificate] 欄序回答。
h與h∘q可同為不連續而criterion_equivalence為是；此等價需本節已認證的surjection與final topology。
查看答案與解釋
(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 0], [3, 0], [4, 1], [5, 0]], quotient_final_property_for_surjective_q)
Wave6第十一層核對=(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 0], [3, 0], [4, 1], [5, 0]], quotient_final_property_for_surjective_q)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-final-continuity · candidate
73. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-final-continuity；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,2,3,5]],"y_points":["a","b"],"q_map":["a","a","a","a","b","a"],"z_points":[0,1],"z_topology":[[],[1],[0,1]],"h_map":[0,1]}。請依 [h_continuous, composite_continuous, criterion_equivalence, h_rows, composite_rows, certificate] 欄序回答。
h與h∘q可同為不連續而criterion_equivalence為是；此等價需本節已認證的surjection與final topology。
查看答案與解釋
(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 0], [2, 0], [3, 0], [4, 1], [5, 0]], quotient_final_property_for_surjective_q)
Wave6第十一層核對=(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 0], [2, 0], [3, 0], [4, 1], [5, 0]], quotient_final_property_for_surjective_q)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-final-continuity · candidate
74. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-final-continuity；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,4,5]],"y_points":["a","b"],"q_map":["a","b","b","b","a","a"],"z_points":[0,1],"z_topology":[[],[1],[0,1]],"h_map":[0,1]}。請依 [h_continuous, composite_continuous, criterion_equivalence, h_rows, composite_rows, certificate] 欄序回答。
h與h∘q可同為不連續而criterion_equivalence為是；此等價需本節已認證的surjection與final topology。
查看答案與解釋
(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 1], [3, 1], [4, 0], [5, 0]], quotient_final_property_for_surjective_q)
Wave6第十一層核對=(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 1], [3, 1], [4, 0], [5, 0]], quotient_final_property_for_surjective_q)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-final-continuity · candidate
75. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-final-continuity；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,4,5]],"y_points":["a","b"],"q_map":["a","a","b","b","a","a"],"z_points":[0,1],"z_topology":[[],[1],[0,1]],"h_map":[0,1]}。請依 [h_continuous, composite_continuous, criterion_equivalence, h_rows, composite_rows, certificate] 欄序回答。
h與h∘q可同為不連續而criterion_equivalence為是；此等價需本節已認證的surjection與final topology。
查看答案與解釋
(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 0], [2, 1], [3, 1], [4, 0], [5, 0]], quotient_final_property_for_surjective_q)
Wave6第十一層核對=(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 0], [2, 1], [3, 1], [4, 0], [5, 0]], quotient_final_property_for_surjective_q)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-final-continuity · candidate
76. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-boundary；資料={"mode":"non_surjective","model":{"x_points":[0,1,2,3],"x_topology":[[],[0],[0,1,2,3]],"y_points":["y0","y1","y2","y3","y4"],"q_map":["y0","y1","y2","y3"]}}。請依 [mode, fibers, surjective, final_topology, final_topology_exists, quotient_map_claim, boundary] 欄序回答。
四種mode為7/8/7/7欄。非滿射仍由逆像iff定義final topology，但依本節慣例不是quotient map；僅有continuity不足以唯一指定final topology。
查看答案與解釋
(non_surjective, [[y0, [0]], [y1, [1]], [y2, [2]], [y3, [3]], [y4, []]], 否, [[y0, y1, y2, y3, y4], [y0, y1, y2, y3], [y0, y4], [y0], [y4], []], 是, 否, preimage_defined_final_topology_exists_but_map_is_not_a_quotient_map_by_this_convention)
Wave6第十一層核對=(non_surjective, [[y0, [0]], [y1, [1]], [y2, [2]], [y3, [3]], [y4, []]], 否, [[y0, y1, y2, y3, y4], [y0, y1, y2, y3], [y0, y4], [y0], [y4], []], 是, 否, preimage_defined_final_topology_exists_but_map_is_not_a_quotient_map_by_this_convention)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-topology-boundary · candidate
77. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-boundary；資料={"mode":"open_image_error","model":{"x_points":[0,1,2,3,4],"x_topology":[[],[0],[0,1,2,3,4]],"y_points":["a","b"],"q_map":["a","a","a","b","b"],"subset":[0]}}。請依 [mode, source_subset, source_open, image, image_preimage, image_open, automatic_open_map_claim, boundary] 欄序回答。
四種mode為7/8/7/7欄。非滿射仍由逆像iff定義final topology，但依本節慣例不是quotient map；僅有continuity不足以唯一指定final topology。
查看答案與解釋
(open_image_error, [0], 是, [a], [0, 1, 2], 否, 否, quotient_maps_need_not_be_open)
Wave6第十一層核對=(open_image_error, [0], 是, [a], [0, 1, 2], 否, 否, quotient_maps_need_not_be_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-topology-boundary · candidate
78. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-boundary；資料={"mode":"coarser_target","model":{"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,2]],"y_points":["a","b"],"q_map":["a","a","a","b","b","b"],"candidate_topology":[[],["a","b"]]}}。請依 [mode, candidate_topology, final_topology, q_continuous, properly_coarser, final_topology_identification_claim, boundary] 欄序回答。
四種mode為7/8/7/7欄。非滿射仍由逆像iff定義final topology，但依本節慣例不是quotient map；僅有continuity不足以唯一指定final topology。
查看答案與解釋
(coarser_target, [[a, b], []], [[a, b], [a], []], 是, 是, 否, continuity_alone_does_not_identify_the_final_topology)
Wave6第十一層核對=(coarser_target, [[a, b], []], [[a, b], [a], []], 是, 是, 否, continuity_alone_does_not_identify_the_final_topology)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-topology-boundary · candidate
79. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-boundary；資料={"mode":"fiber_split","model":{"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5]],"y_points":["a","b"],"q_map":["a","a","b","b","b","b"],"subset":[0]}}。請依 [mode, source_subset, image, saturation, saturated, full_preimage_claim, boundary] 欄序回答。
四種mode為7/8/7/7欄。非滿射仍由逆像iff定義final topology，但依本節慣例不是quotient map；僅有continuity不足以唯一指定final topology。
查看答案與解釋
(fiber_split, [0], [a], [0, 1], 否, 否, only_saturated_subsets_are_full_preimages)
Wave6第十一層核對=(fiber_split, [0], [a], [0, 1], 否, 否, only_saturated_subsets_are_full_preimages)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-topology-boundary · candidate
80. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-boundary；資料={"mode":"non_surjective","model":{"x_points":[0,1,2,3],"x_topology":[[],[1],[0,1,2,3]],"y_points":["y0","y1","y2","y3","y4"],"q_map":["y0","y1","y2","y3"]}}。請依 [mode, fibers, surjective, final_topology, final_topology_exists, quotient_map_claim, boundary] 欄序回答。
四種mode為7/8/7/7欄。非滿射仍由逆像iff定義final topology，但依本節慣例不是quotient map；僅有continuity不足以唯一指定final topology。
查看答案與解釋
(non_surjective, [[y0, [0]], [y1, [1]], [y2, [2]], [y3, [3]], [y4, []]], 否, [[y0, y1, y2, y3, y4], [y0, y1, y2, y3], [y1, y4], [y1], [y4], []], 是, 否, preimage_defined_final_topology_exists_but_map_is_not_a_quotient_map_by_this_convention)
Wave6第十一層核對=(non_surjective, [[y0, [0]], [y1, [1]], [y2, [2]], [y3, [3]], [y4, []]], 否, [[y0, y1, y2, y3, y4], [y0, y1, y2, y3], [y1, y4], [y1], [y4], []], 是, 否, preimage_defined_final_topology_exists_but_map_is_not_a_quotient_map_by_this_convention)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-topology-boundary · candidate
81. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-boundary；資料={"mode":"open_image_error","model":{"x_points":[0,1,2,3,4],"x_topology":[[],[1],[0,1,2,3,4]],"y_points":["a","b"],"q_map":["a","a","a","b","b"],"subset":[1]}}。請依 [mode, source_subset, source_open, image, image_preimage, image_open, automatic_open_map_claim, boundary] 欄序回答。
四種mode為7/8/7/7欄。非滿射仍由逆像iff定義final topology，但依本節慣例不是quotient map；僅有continuity不足以唯一指定final topology。
查看答案與解釋
(open_image_error, [1], 是, [a], [0, 1, 2], 否, 否, quotient_maps_need_not_be_open)
Wave6第十一層核對=(open_image_error, [1], 是, [a], [0, 1, 2], 否, 否, quotient_maps_need_not_be_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-topology-boundary · candidate
82. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-boundary；資料={"mode":"coarser_target","model":{"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,2,3]],"y_points":["a","b"],"q_map":["a","a","a","a","b","b"],"candidate_topology":[[],["a","b"]]}}。請依 [mode, candidate_topology, final_topology, q_continuous, properly_coarser, final_topology_identification_claim, boundary] 欄序回答。
四種mode為7/8/7/7欄。非滿射仍由逆像iff定義final topology，但依本節慣例不是quotient map；僅有continuity不足以唯一指定final topology。
查看答案與解釋
(coarser_target, [[a, b], []], [[a, b], [a], []], 是, 是, 否, continuity_alone_does_not_identify_the_final_topology)
Wave6第十一層核對=(coarser_target, [[a, b], []], [[a, b], [a], []], 是, 是, 否, continuity_alone_does_not_identify_the_final_topology)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-topology-boundary · candidate
83. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-boundary；資料={"mode":"fiber_split","model":{"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5]],"y_points":["a","b"],"q_map":["a","b","a","b","b","b"],"subset":[0]}}。請依 [mode, source_subset, image, saturation, saturated, full_preimage_claim, boundary] 欄序回答。
四種mode為7/8/7/7欄。非滿射仍由逆像iff定義final topology，但依本節慣例不是quotient map；僅有continuity不足以唯一指定final topology。
查看答案與解釋
(fiber_split, [0], [a], [0, 2], 否, 否, only_saturated_subsets_are_full_preimages)
Wave6第十一層核對=(fiber_split, [0], [a], [0, 2], 否, 否, only_saturated_subsets_are_full_preimages)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-topology-boundary · candidate
84. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-boundary；資料={"mode":"non_surjective","model":{"x_points":[0,1,2,3],"x_topology":[[],[0,1],[0,1,2,3]],"y_points":["y0","y1","y2","y3","y4"],"q_map":["y0","y1","y2","y3"]}}。請依 [mode, fibers, surjective, final_topology, final_topology_exists, quotient_map_claim, boundary] 欄序回答。
四種mode為7/8/7/7欄。非滿射仍由逆像iff定義final topology，但依本節慣例不是quotient map；僅有continuity不足以唯一指定final topology。
查看答案與解釋
(non_surjective, [[y0, [0]], [y1, [1]], [y2, [2]], [y3, [3]], [y4, []]], 否, [[y0, y1, y2, y3, y4], [y0, y1, y2, y3], [y0, y1, y4], [y0, y1], [y4], []], 是, 否, preimage_defined_final_topology_exists_but_map_is_not_a_quotient_map_by_this_convention)
Wave6第十一層核對=(non_surjective, [[y0, [0]], [y1, [1]], [y2, [2]], [y3, [3]], [y4, []]], 否, [[y0, y1, y2, y3, y4], [y0, y1, y2, y3], [y0, y1, y4], [y0, y1], [y4], []], 是, 否, preimage_defined_final_topology_exists_but_map_is_not_a_quotient_map_by_this_convention)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-topology-boundary · candidate
85. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-boundary；資料={"mode":"open_image_error","model":{"x_points":[0,1,2,3,4],"x_topology":[[],[0,1],[0,1,2,3,4]],"y_points":["a","b"],"q_map":["a","a","a","b","b"],"subset":[0,1]}}。請依 [mode, source_subset, source_open, image, image_preimage, image_open, automatic_open_map_claim, boundary] 欄序回答。
四種mode為7/8/7/7欄。非滿射仍由逆像iff定義final topology，但依本節慣例不是quotient map；僅有continuity不足以唯一指定final topology。
查看答案與解釋
(open_image_error, [0, 1], 是, [a], [0, 1, 2], 否, 否, quotient_maps_need_not_be_open)
Wave6第十一層核對=(open_image_error, [0, 1], 是, [a], [0, 1, 2], 否, 否, quotient_maps_need_not_be_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-topology-boundary · candidate
86. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-boundary；資料={"mode":"coarser_target","model":{"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,2,4]],"y_points":["a","b"],"q_map":["a","a","a","b","a","b"],"candidate_topology":[[],["a","b"]]}}。請依 [mode, candidate_topology, final_topology, q_continuous, properly_coarser, final_topology_identification_claim, boundary] 欄序回答。
四種mode為7/8/7/7欄。非滿射仍由逆像iff定義final topology，但依本節慣例不是quotient map；僅有continuity不足以唯一指定final topology。
查看答案與解釋
(coarser_target, [[a, b], []], [[a, b], [a], []], 是, 是, 否, continuity_alone_does_not_identify_the_final_topology)
Wave6第十一層核對=(coarser_target, [[a, b], []], [[a, b], [a], []], 是, 是, 否, continuity_alone_does_not_identify_the_final_topology)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-topology-boundary · candidate
87. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-boundary；資料={"mode":"fiber_split","model":{"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5]],"y_points":["a","b"],"q_map":["a","a","a","b","b","b"],"subset":[0]}}。請依 [mode, source_subset, image, saturation, saturated, full_preimage_claim, boundary] 欄序回答。
四種mode為7/8/7/7欄。非滿射仍由逆像iff定義final topology，但依本節慣例不是quotient map；僅有continuity不足以唯一指定final topology。
查看答案與解釋
(fiber_split, [0], [a], [0, 1, 2], 否, 否, only_saturated_subsets_are_full_preimages)
Wave6第十一層核對=(fiber_split, [0], [a], [0, 1, 2], 否, 否, only_saturated_subsets_are_full_preimages)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-topology-boundary · candidate
88. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-boundary；資料={"mode":"non_surjective","model":{"x_points":[0,1,2,3],"x_topology":[[],[2],[0,1,2,3]],"y_points":["y0","y1","y2","y3","y4"],"q_map":["y0","y1","y2","y3"]}}。請依 [mode, fibers, surjective, final_topology, final_topology_exists, quotient_map_claim, boundary] 欄序回答。
四種mode為7/8/7/7欄。非滿射仍由逆像iff定義final topology，但依本節慣例不是quotient map；僅有continuity不足以唯一指定final topology。
查看答案與解釋
(non_surjective, [[y0, [0]], [y1, [1]], [y2, [2]], [y3, [3]], [y4, []]], 否, [[y0, y1, y2, y3, y4], [y0, y1, y2, y3], [y2, y4], [y2], [y4], []], 是, 否, preimage_defined_final_topology_exists_but_map_is_not_a_quotient_map_by_this_convention)
Wave6第十一層核對=(non_surjective, [[y0, [0]], [y1, [1]], [y2, [2]], [y3, [3]], [y4, []]], 否, [[y0, y1, y2, y3, y4], [y0, y1, y2, y3], [y2, y4], [y2], [y4], []], 是, 否, preimage_defined_final_topology_exists_but_map_is_not_a_quotient_map_by_this_convention)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-topology-boundary · candidate
89. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-boundary；資料={"mode":"open_image_error","model":{"x_points":[0,1,2,3,4],"x_topology":[[],[2],[0,1,2,3,4]],"y_points":["a","b"],"q_map":["a","a","a","b","b"],"subset":[2]}}。請依 [mode, source_subset, source_open, image, image_preimage, image_open, automatic_open_map_claim, boundary] 欄序回答。
四種mode為7/8/7/7欄。非滿射仍由逆像iff定義final topology，但依本節慣例不是quotient map；僅有continuity不足以唯一指定final topology。
查看答案與解釋
(open_image_error, [2], 是, [a], [0, 1, 2], 否, 否, quotient_maps_need_not_be_open)
Wave6第十一層核對=(open_image_error, [2], 是, [a], [0, 1, 2], 否, 否, quotient_maps_need_not_be_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-topology-boundary · candidate
90. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-boundary；資料={"mode":"coarser_target","model":{"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,2,3,4]],"y_points":["a","b"],"q_map":["a","a","a","a","a","b"],"candidate_topology":[[],["a","b"]]}}。請依 [mode, candidate_topology, final_topology, q_continuous, properly_coarser, final_topology_identification_claim, boundary] 欄序回答。
四種mode為7/8/7/7欄。非滿射仍由逆像iff定義final topology，但依本節慣例不是quotient map；僅有continuity不足以唯一指定final topology。
查看答案與解釋
(coarser_target, [[a, b], []], [[a, b], [a], []], 是, 是, 否, continuity_alone_does_not_identify_the_final_topology)
Wave6第十一層核對=(coarser_target, [[a, b], []], [[a, b], [a], []], 是, 是, 否, continuity_alone_does_not_identify_the_final_topology)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-topology-boundary · candidate
91. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-boundary；資料={"mode":"fiber_split","model":{"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5]],"y_points":["a","b"],"q_map":["a","b","b","a","b","b"],"subset":[0]}}。請依 [mode, source_subset, image, saturation, saturated, full_preimage_claim, boundary] 欄序回答。
四種mode為7/8/7/7欄。非滿射仍由逆像iff定義final topology，但依本節慣例不是quotient map；僅有continuity不足以唯一指定final topology。
查看答案與解釋
(fiber_split, [0], [a], [0, 3], 否, 否, only_saturated_subsets_are_full_preimages)
Wave6第十一層核對=(fiber_split, [0], [a], [0, 3], 否, 否, only_saturated_subsets_are_full_preimages)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-topology-boundary · candidate
92. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-boundary；資料={"mode":"non_surjective","model":{"x_points":[0,1,2,3],"x_topology":[[],[0,2],[0,1,2,3]],"y_points":["y0","y1","y2","y3","y4"],"q_map":["y0","y1","y2","y3"]}}。請依 [mode, fibers, surjective, final_topology, final_topology_exists, quotient_map_claim, boundary] 欄序回答。
四種mode為7/8/7/7欄。非滿射仍由逆像iff定義final topology，但依本節慣例不是quotient map；僅有continuity不足以唯一指定final topology。
查看答案與解釋
(non_surjective, [[y0, [0]], [y1, [1]], [y2, [2]], [y3, [3]], [y4, []]], 否, [[y0, y1, y2, y3, y4], [y0, y1, y2, y3], [y0, y2, y4], [y0, y2], [y4], []], 是, 否, preimage_defined_final_topology_exists_but_map_is_not_a_quotient_map_by_this_convention)
Wave6第十一層核對=(non_surjective, [[y0, [0]], [y1, [1]], [y2, [2]], [y3, [3]], [y4, []]], 否, [[y0, y1, y2, y3, y4], [y0, y1, y2, y3], [y0, y2, y4], [y0, y2], [y4], []], 是, 否, preimage_defined_final_topology_exists_but_map_is_not_a_quotient_map_by_this_convention)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-topology-boundary · candidate
93. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-boundary；資料={"mode":"open_image_error","model":{"x_points":[0,1,2,3,4],"x_topology":[[],[0,2],[0,1,2,3,4]],"y_points":["a","b"],"q_map":["a","a","a","b","b"],"subset":[0,2]}}。請依 [mode, source_subset, source_open, image, image_preimage, image_open, automatic_open_map_claim, boundary] 欄序回答。
四種mode為7/8/7/7欄。非滿射仍由逆像iff定義final topology，但依本節慣例不是quotient map；僅有continuity不足以唯一指定final topology。
查看答案與解釋
(open_image_error, [0, 2], 是, [a], [0, 1, 2], 否, 否, quotient_maps_need_not_be_open)
Wave6第十一層核對=(open_image_error, [0, 2], 是, [a], [0, 1, 2], 否, 否, quotient_maps_need_not_be_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-topology-boundary · candidate
94. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-boundary；資料={"mode":"coarser_target","model":{"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,2,5]],"y_points":["a","b"],"q_map":["a","a","a","b","b","a"],"candidate_topology":[[],["a","b"]]}}。請依 [mode, candidate_topology, final_topology, q_continuous, properly_coarser, final_topology_identification_claim, boundary] 欄序回答。
四種mode為7/8/7/7欄。非滿射仍由逆像iff定義final topology，但依本節慣例不是quotient map；僅有continuity不足以唯一指定final topology。
查看答案與解釋
(coarser_target, [[a, b], []], [[a, b], [a], []], 是, 是, 否, continuity_alone_does_not_identify_the_final_topology)
Wave6第十一層核對=(coarser_target, [[a, b], []], [[a, b], [a], []], 是, 是, 否, continuity_alone_does_not_identify_the_final_topology)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-topology-boundary · candidate
95. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-boundary；資料={"mode":"fiber_split","model":{"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5]],"y_points":["a","b"],"q_map":["a","a","b","a","b","b"],"subset":[0]}}。請依 [mode, source_subset, image, saturation, saturated, full_preimage_claim, boundary] 欄序回答。
四種mode為7/8/7/7欄。非滿射仍由逆像iff定義final topology，但依本節慣例不是quotient map；僅有continuity不足以唯一指定final topology。
查看答案與解釋
(fiber_split, [0], [a], [0, 1, 3], 否, 否, only_saturated_subsets_are_full_preimages)
Wave6第十一層核對=(fiber_split, [0], [a], [0, 1, 3], 否, 否, only_saturated_subsets_are_full_preimages)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-topology-boundary · candidate
96. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-boundary；資料={"mode":"non_surjective","model":{"x_points":[0,1,2,3],"x_topology":[[],[1,2],[0,1,2,3]],"y_points":["y0","y1","y2","y3","y4"],"q_map":["y0","y1","y2","y3"]}}。請依 [mode, fibers, surjective, final_topology, final_topology_exists, quotient_map_claim, boundary] 欄序回答。
四種mode為7/8/7/7欄。非滿射仍由逆像iff定義final topology，但依本節慣例不是quotient map；僅有continuity不足以唯一指定final topology。
查看答案與解釋
(non_surjective, [[y0, [0]], [y1, [1]], [y2, [2]], [y3, [3]], [y4, []]], 否, [[y0, y1, y2, y3, y4], [y0, y1, y2, y3], [y1, y2, y4], [y1, y2], [y4], []], 是, 否, preimage_defined_final_topology_exists_but_map_is_not_a_quotient_map_by_this_convention)
Wave6第十一層核對=(non_surjective, [[y0, [0]], [y1, [1]], [y2, [2]], [y3, [3]], [y4, []]], 否, [[y0, y1, y2, y3, y4], [y0, y1, y2, y3], [y1, y2, y4], [y1, y2], [y4], []], 是, 否, preimage_defined_final_topology_exists_but_map_is_not_a_quotient_map_by_this_convention)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-topology-boundary · candidate
97. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-boundary；資料={"mode":"open_image_error","model":{"x_points":[0,1,2,3,4],"x_topology":[[],[1,2],[0,1,2,3,4]],"y_points":["a","b"],"q_map":["a","a","a","b","b"],"subset":[1,2]}}。請依 [mode, source_subset, source_open, image, image_preimage, image_open, automatic_open_map_claim, boundary] 欄序回答。
四種mode為7/8/7/7欄。非滿射仍由逆像iff定義final topology，但依本節慣例不是quotient map；僅有continuity不足以唯一指定final topology。
查看答案與解釋
(open_image_error, [1, 2], 是, [a], [0, 1, 2], 否, 否, quotient_maps_need_not_be_open)
Wave6第十一層核對=(open_image_error, [1, 2], 是, [a], [0, 1, 2], 否, 否, quotient_maps_need_not_be_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-topology-boundary · candidate
98. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-boundary；資料={"mode":"coarser_target","model":{"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,2,3,5]],"y_points":["a","b"],"q_map":["a","a","a","a","b","a"],"candidate_topology":[[],["a","b"]]}}。請依 [mode, candidate_topology, final_topology, q_continuous, properly_coarser, final_topology_identification_claim, boundary] 欄序回答。
四種mode為7/8/7/7欄。非滿射仍由逆像iff定義final topology，但依本節慣例不是quotient map；僅有continuity不足以唯一指定final topology。
查看答案與解釋
(coarser_target, [[a, b], []], [[a, b], [a], []], 是, 是, 否, continuity_alone_does_not_identify_the_final_topology)
Wave6第十一層核對=(coarser_target, [[a, b], []], [[a, b], [a], []], 是, 是, 否, continuity_alone_does_not_identify_the_final_topology)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-topology-boundary · candidate
99. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-boundary；資料={"mode":"fiber_split","model":{"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5]],"y_points":["a","b"],"q_map":["a","b","a","a","b","b"],"subset":[0]}}。請依 [mode, source_subset, image, saturation, saturated, full_preimage_claim, boundary] 欄序回答。
四種mode為7/8/7/7欄。非滿射仍由逆像iff定義final topology，但依本節慣例不是quotient map；僅有continuity不足以唯一指定final topology。
查看答案與解釋
(fiber_split, [0], [a], [0, 2, 3], 否, 否, only_saturated_subsets_are_full_preimages)
Wave6第十一層核對=(fiber_split, [0], [a], [0, 2, 3], 否, 否, only_saturated_subsets_are_full_preimages)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-topology-boundary · candidate
100. 商拓撲
finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-boundary；資料={"mode":"non_surjective","model":{"x_points":[0,1,2,3],"x_topology":[[],[0,1,2],[0,1,2,3]],"y_points":["y0","y1","y2","y3","y4"],"q_map":["y0","y1","y2","y3"]}}。請依 [mode, fibers, surjective, final_topology, final_topology_exists, quotient_map_claim, boundary] 欄序回答。
四種mode為7/8/7/7欄。非滿射仍由逆像iff定義final topology，但依本節慣例不是quotient map；僅有continuity不足以唯一指定final topology。
查看答案與解釋
(non_surjective, [[y0, [0]], [y1, [1]], [y2, [2]], [y3, [3]], [y4, []]], 否, [[y0, y1, y2, y3, y4], [y0, y1, y2, y3], [y0, y1, y2, y4], [y0, y1, y2], [y4], []], 是, 否, preimage_defined_final_topology_exists_but_map_is_not_a_quotient_map_by_this_convention)
Wave6第十一層核對=(non_surjective, [[y0, [0]], [y1, [1]], [y2, [2]], [y3, [3]], [y4, []]], 否, [[y0, y1, y2, y3, y4], [y0, y1, y2, y3], [y0, y1, y2, y4], [y0, y1, y2], [y4], []], 是, 否, preimage_defined_final_topology_exists_but_map_is_not_a_quotient_map_by_this_convention)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。
本題逐步詳解（AI 二次覆核）
商拓撲 · qf-mod48-quotient-topology-boundary · candidate
原始題目 JSONL · 驗收報告