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-20261013-advance-20261019-r03-topological-continuity-foundations · 2026-10-13 · 100 題
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。
(4, 4, [], [], 是)
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。
拓撲連續映射 · qf-ext19-continuity-single-preimage · candidate
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。
(4, 4, [1], [0], 否)
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。
拓撲連續映射 · qf-ext19-continuity-single-preimage · candidate
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。
(4, 4, [1], [2], 是)
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。
拓撲連續映射 · qf-ext19-continuity-single-preimage · candidate
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。
(4, 4, [0, 2, 3], [0, 1, 3], 是)
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。
拓撲連續映射 · qf-ext19-continuity-single-preimage · candidate
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。
(4, 4, [2], [1], 否)
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。
拓撲連續映射 · qf-ext19-continuity-single-preimage · candidate
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。
(4, 4, [], [], 是)
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。
拓撲連續映射 · qf-ext19-continuity-single-preimage · candidate
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。
(4, 4, [1, 2], [0, 1], 否)
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。
拓撲連續映射 · qf-ext19-continuity-single-preimage · candidate
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。
(4, 4, [2, 3], [0, 3], 否)
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。
拓撲連續映射 · qf-ext19-continuity-single-preimage · candidate
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。
(4, 4, [3], [1], 否)
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。
拓撲連續映射 · qf-ext19-continuity-single-preimage · candidate
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。
(4, 4, [0, 1, 2, 3], [0, 1, 2, 3], 是)
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。
拓撲連續映射 · qf-ext19-continuity-single-preimage · candidate
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。
(4, 4, [1, 3], [1, 3], 否)
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。
拓撲連續映射 · qf-ext19-continuity-single-preimage · candidate
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。
(4, 4, [3], [0], 否)
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。
拓撲連續映射 · qf-ext19-continuity-single-preimage · candidate
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。
(4, 4, [2, 3], [2, 3], 否)
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。
拓撲連續映射 · qf-ext19-continuity-single-preimage · candidate
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。
(4, 4, [1, 2, 3], [0, 2, 3], 否)
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。
拓撲連續映射 · qf-ext19-continuity-single-preimage · candidate
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。
(4, 4, [1, 2, 3], [0, 2, 3], 是)
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。
拓撲連續映射 · qf-ext19-continuity-single-preimage · candidate
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。
(4, 4, [], [], 是)
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。
拓撲連續映射 · qf-ext19-continuity-single-preimage · candidate
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。
(4, 4, [], [], 是)
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。
拓撲連續映射 · qf-ext19-continuity-single-preimage · candidate
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。
(4, 4, [0, 1], [0, 3], 否)
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。
拓撲連續映射 · qf-ext19-continuity-single-preimage · candidate
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。
(4, 4, [1], [1], 否)
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。
拓撲連續映射 · qf-ext19-continuity-single-preimage · candidate
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。
(4, 4, [0, 1, 2, 3], [0, 1, 2, 3], 是)
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。
拓撲連續映射 · qf-ext19-continuity-single-preimage · candidate
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。
(4, 4, [2], [2], 否)
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。
拓撲連續映射 · qf-ext19-continuity-single-preimage · candidate
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。
(4, 4, [1], [0], 否)
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。
拓撲連續映射 · qf-ext19-continuity-single-preimage · candidate
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。
(4, 4, [1, 2], [0, 2], 否)
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。
拓撲連續映射 · qf-ext19-continuity-single-preimage · candidate
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。
(4, 4, [1, 2, 3], [0, 1, 2], 否)
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。
拓撲連續映射 · qf-ext19-continuity-single-preimage · candidate
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。
(3, 3, [], [], 是)
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。
拓撲連續映射 · qf-ext19-continuity-single-preimage · candidate
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。
([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)
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。
拓撲連續映射 · qf-ext19-continuity-full-audit · candidate
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。
([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)
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。
拓撲連續映射 · qf-ext19-continuity-full-audit · candidate
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。
([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)
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。
拓撲連續映射 · qf-ext19-continuity-full-audit · candidate
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。
([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)
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。
拓撲連續映射 · qf-ext19-continuity-full-audit · candidate
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。
([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)
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。
拓撲連續映射 · qf-ext19-continuity-full-audit · candidate
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。
([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)
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。
拓撲連續映射 · qf-ext19-continuity-full-audit · candidate
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。
([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)
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。
拓撲連續映射 · qf-ext19-continuity-full-audit · candidate
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。
([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)
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。
拓撲連續映射 · qf-ext19-continuity-full-audit · candidate
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。
([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)
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。
拓撲連續映射 · qf-ext19-continuity-full-audit · candidate
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。
([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)
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。
拓撲連續映射 · qf-ext19-continuity-full-audit · candidate
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。
([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)
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。
拓撲連續映射 · qf-ext19-continuity-full-audit · candidate
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。
([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)
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。
拓撲連續映射 · qf-ext19-continuity-full-audit · candidate
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。
([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)
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。
拓撲連續映射 · qf-ext19-continuity-full-audit · candidate
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。
([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)
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。
拓撲連續映射 · qf-ext19-continuity-full-audit · candidate
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。
([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)
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。
拓撲連續映射 · qf-ext19-continuity-full-audit · candidate
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。
([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)
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。
拓撲連續映射 · qf-ext19-continuity-full-audit · candidate
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。
([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)
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。
拓撲連續映射 · qf-ext19-continuity-full-audit · candidate
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。
([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)
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。
拓撲連續映射 · qf-ext19-continuity-full-audit · candidate
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。
([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)
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。
拓撲連續映射 · qf-ext19-continuity-full-audit · candidate
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。
([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)
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。
拓撲連續映射 · qf-ext19-continuity-full-audit · candidate
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。
([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)
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。
拓撲連續映射 · qf-ext19-continuity-full-audit · candidate
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。
([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)
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。
拓撲連續映射 · qf-ext19-continuity-full-audit · candidate
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。
([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)
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。
拓撲連續映射 · qf-ext19-continuity-full-audit · candidate
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。
([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)
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。
拓撲連續映射 · qf-ext19-continuity-full-audit · candidate
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。
([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)
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。
拓撲連續映射 · qf-ext19-continuity-full-audit · candidate
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。
([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]])
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。
拓撲連續映射 · qf-ext19-continuity-composition · candidate
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。
([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]])
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。
拓撲連續映射 · qf-ext19-continuity-composition · candidate
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。
([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]])
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。
拓撲連續映射 · qf-ext19-continuity-composition · candidate
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。
([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]])
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。
拓撲連續映射 · qf-ext19-continuity-composition · candidate
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。
([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]])
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。
拓撲連續映射 · qf-ext19-continuity-composition · candidate
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。
([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]])
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。
拓撲連續映射 · qf-ext19-continuity-composition · candidate
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。
([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]])
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。
拓撲連續映射 · qf-ext19-continuity-composition · candidate
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。
([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]])
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。
拓撲連續映射 · qf-ext19-continuity-composition · candidate
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。
([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]])
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。
拓撲連續映射 · qf-ext19-continuity-composition · candidate
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。
([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]])
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。
拓撲連續映射 · qf-ext19-continuity-composition · candidate
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。
([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]])
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。
拓撲連續映射 · qf-ext19-continuity-composition · candidate
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。
([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]])
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。
拓撲連續映射 · qf-ext19-continuity-composition · candidate
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。
([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]])
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。
拓撲連續映射 · qf-ext19-continuity-composition · candidate
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。
([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]])
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。
拓撲連續映射 · qf-ext19-continuity-composition · candidate
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。
([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]])
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。
拓撲連續映射 · qf-ext19-continuity-composition · candidate
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。
([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]])
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。
拓撲連續映射 · qf-ext19-continuity-composition · candidate
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。
([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]])
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。
拓撲連續映射 · qf-ext19-continuity-composition · candidate
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。
([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]])
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。
拓撲連續映射 · qf-ext19-continuity-composition · candidate
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。
([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]])
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。
拓撲連續映射 · qf-ext19-continuity-composition · candidate
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。
([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]])
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。
拓撲連續映射 · qf-ext19-continuity-composition · candidate
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。
([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]])
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。
拓撲連續映射 · qf-ext19-continuity-composition · candidate
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。
([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]])
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。
拓撲連續映射 · qf-ext19-continuity-composition · candidate
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。
([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]])
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。
拓撲連續映射 · qf-ext19-continuity-composition · candidate
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。
([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]])
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。
拓撲連續映射 · qf-ext19-continuity-composition · candidate
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。
([0, 1, 2], [0, 1, 2], [0, 1, 2], 否, 是, 是, [[[], [], 是], [[0, 1, 2], [0, 1, 2], 是]])
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。
拓撲連續映射 · qf-ext19-continuity-composition · candidate
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。
([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)
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。
拓撲連續映射 · qf-ext19-continuity-open-map-contrast · candidate
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。
([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)
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。
拓撲連續映射 · qf-ext19-continuity-open-map-contrast · candidate
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。
([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)
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。
拓撲連續映射 · qf-ext19-continuity-open-map-contrast · candidate
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。
([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)
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。
拓撲連續映射 · qf-ext19-continuity-open-map-contrast · candidate
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。
([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)
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。
拓撲連續映射 · qf-ext19-continuity-open-map-contrast · candidate
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。
([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)
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。
拓撲連續映射 · qf-ext19-continuity-open-map-contrast · candidate
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。
([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)
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。
拓撲連續映射 · qf-ext19-continuity-open-map-contrast · candidate
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。
([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)
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。
拓撲連續映射 · qf-ext19-continuity-open-map-contrast · candidate
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。
([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)
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。
拓撲連續映射 · qf-ext19-continuity-open-map-contrast · candidate
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。
([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)
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。
拓撲連續映射 · qf-ext19-continuity-open-map-contrast · candidate
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。
([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)
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。
拓撲連續映射 · qf-ext19-continuity-open-map-contrast · candidate
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。
([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)
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。
拓撲連續映射 · qf-ext19-continuity-open-map-contrast · candidate
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。
([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)
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。
拓撲連續映射 · qf-ext19-continuity-open-map-contrast · candidate
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。
([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)
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。
拓撲連續映射 · qf-ext19-continuity-open-map-contrast · candidate
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。
([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)
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。
拓撲連續映射 · qf-ext19-continuity-open-map-contrast · candidate
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。
([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)
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。
拓撲連續映射 · qf-ext19-continuity-open-map-contrast · candidate
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。
([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)
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。
拓撲連續映射 · qf-ext19-continuity-open-map-contrast · candidate
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。
([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)
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。
拓撲連續映射 · qf-ext19-continuity-open-map-contrast · candidate
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。
([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)
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。
拓撲連續映射 · qf-ext19-continuity-open-map-contrast · candidate
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。
([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)
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。
拓撲連續映射 · qf-ext19-continuity-open-map-contrast · candidate
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。
([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)
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。
拓撲連續映射 · qf-ext19-continuity-open-map-contrast · candidate
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。
([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)
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。
拓撲連續映射 · qf-ext19-continuity-open-map-contrast · candidate
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。
([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)
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。
拓撲連續映射 · qf-ext19-continuity-open-map-contrast · candidate
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。
([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)
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。
拓撲連續映射 · qf-ext19-continuity-open-map-contrast · candidate
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。
([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)
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。
拓撲連續映射 · qf-ext19-continuity-open-map-contrast · candidate