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-20261014-advance-20261103-r05-connected-topological-space-foundations · 2026-10-14 · 100 題
完整有限拓撲與全部clopen/separation候選。操作=connected-separation-audit；資料={"n":5,"topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4]],"left":[0,1],"right":[2,3,4]}。請依 [left,right,valid_separation,classification] 欄序回答。
([0, 1], [2, 3, 4], 否, not_a_separation)
Wave5第三層核對=([0, 1], [2, 3, 4], 否, not_a_separation)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-separation-audit · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-separation-audit；資料={"n":5,"topology":[[],[0],[0,1],[0,1,2],[0,1,2,4],[0,1,2,3,4]],"left":[0,1],"right":[2,3,4]}。請依 [left,right,valid_separation,classification] 欄序回答。
([0, 1], [2, 3, 4], 否, not_a_separation)
Wave5第三層核對=([0, 1], [2, 3, 4], 否, not_a_separation)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-separation-audit · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-separation-audit；資料={"n":5,"topology":[[],[0],[0,1],[0,1,3],[0,1,2,3],[0,1,2,3,4]],"left":[0,1],"right":[2,3,4]}。請依 [left,right,valid_separation,classification] 欄序回答。
([0, 1], [2, 3, 4], 否, not_a_separation)
Wave5第三層核對=([0, 1], [2, 3, 4], 否, not_a_separation)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-separation-audit · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-separation-audit；資料={"n":5,"topology":[[],[0],[0,1],[0,1,3],[0,1,3,4],[0,1,2,3,4]],"left":[0,1],"right":[2,3,4]}。請依 [left,right,valid_separation,classification] 欄序回答。
([0, 1], [2, 3, 4], 否, not_a_separation)
Wave5第三層核對=([0, 1], [2, 3, 4], 否, not_a_separation)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-separation-audit · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-separation-audit；資料={"n":5,"topology":[[],[0],[0,1],[0,1,4],[0,1,2,4],[0,1,2,3,4]],"left":[0,1],"right":[2,3,4]}。請依 [left,right,valid_separation,classification] 欄序回答。
([0, 1], [2, 3, 4], 否, not_a_separation)
Wave5第三層核對=([0, 1], [2, 3, 4], 否, not_a_separation)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-separation-audit · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-separation-audit；資料={"n":5,"topology":[[],[0],[0,1],[0,1,4],[0,1,3,4],[0,1,2,3,4]],"left":[0,1],"right":[2,3,4]}。請依 [left,right,valid_separation,classification] 欄序回答。
([0, 1], [2, 3, 4], 否, not_a_separation)
Wave5第三層核對=([0, 1], [2, 3, 4], 否, not_a_separation)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-separation-audit · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-separation-audit；資料={"n":5,"topology":[[],[0],[0,2],[0,1,2],[0,1,2,3],[0,1,2,3,4]],"left":[0,2],"right":[1,3,4]}。請依 [left,right,valid_separation,classification] 欄序回答。
([0, 2], [1, 3, 4], 否, not_a_separation)
Wave5第三層核對=([0, 2], [1, 3, 4], 否, not_a_separation)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-separation-audit · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-separation-audit；資料={"n":5,"topology":[[],[0],[0,2],[0,1,2],[0,1,2,4],[0,1,2,3,4]],"left":[0,2],"right":[1,3,4]}。請依 [left,right,valid_separation,classification] 欄序回答。
([0, 2], [1, 3, 4], 否, not_a_separation)
Wave5第三層核對=([0, 2], [1, 3, 4], 否, not_a_separation)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-separation-audit · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-separation-audit；資料={"n":5,"topology":[[],[0],[0,2],[0,2,3],[0,1,2,3],[0,1,2,3,4]],"left":[0,2],"right":[1,3,4]}。請依 [left,right,valid_separation,classification] 欄序回答。
([0, 2], [1, 3, 4], 否, not_a_separation)
Wave5第三層核對=([0, 2], [1, 3, 4], 否, not_a_separation)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-separation-audit · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-separation-audit；資料={"n":5,"topology":[[],[0],[0,2],[0,2,3],[0,2,3,4],[0,1,2,3,4]],"left":[0,2],"right":[1,3,4]}。請依 [left,right,valid_separation,classification] 欄序回答。
([0, 2], [1, 3, 4], 否, not_a_separation)
Wave5第三層核對=([0, 2], [1, 3, 4], 否, not_a_separation)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-separation-audit · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-separation-audit；資料={"n":5,"topology":[[],[0],[0,2],[0,2,4],[0,1,2,4],[0,1,2,3,4]],"left":[0,2],"right":[1,3,4]}。請依 [left,right,valid_separation,classification] 欄序回答。
([0, 2], [1, 3, 4], 否, not_a_separation)
Wave5第三層核對=([0, 2], [1, 3, 4], 否, not_a_separation)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-separation-audit · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-separation-audit；資料={"n":5,"topology":[[],[0],[0,2],[0,2,4],[0,2,3,4],[0,1,2,3,4]],"left":[0,2],"right":[1,3,4]}。請依 [left,right,valid_separation,classification] 欄序回答。
([0, 2], [1, 3, 4], 否, not_a_separation)
Wave5第三層核對=([0, 2], [1, 3, 4], 否, not_a_separation)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-separation-audit · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-separation-audit；資料={"n":5,"topology":[[],[0],[0,3],[0,1,3],[0,1,2,3],[0,1,2,3,4]],"left":[0,3],"right":[1,2,4]}。請依 [left,right,valid_separation,classification] 欄序回答。
([0, 3], [1, 2, 4], 否, not_a_separation)
Wave5第三層核對=([0, 3], [1, 2, 4], 否, not_a_separation)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-separation-audit · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-separation-audit；資料={"n":5,"topology":[[],[0],[0,3],[0,1,3],[0,1,3,4],[0,1,2,3,4]],"left":[0,3],"right":[1,2,4]}。請依 [left,right,valid_separation,classification] 欄序回答。
([0, 3], [1, 2, 4], 否, not_a_separation)
Wave5第三層核對=([0, 3], [1, 2, 4], 否, not_a_separation)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-separation-audit · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-separation-audit；資料={"n":5,"topology":[[],[0],[0,3],[0,2,3],[0,1,2,3],[0,1,2,3,4]],"left":[0,3],"right":[1,2,4]}。請依 [left,right,valid_separation,classification] 欄序回答。
([0, 3], [1, 2, 4], 否, not_a_separation)
Wave5第三層核對=([0, 3], [1, 2, 4], 否, not_a_separation)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-separation-audit · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-separation-audit；資料={"n":5,"topology":[[],[0],[0,3],[0,2,3],[0,2,3,4],[0,1,2,3,4]],"left":[0,3],"right":[1,2,4]}。請依 [left,right,valid_separation,classification] 欄序回答。
([0, 3], [1, 2, 4], 否, not_a_separation)
Wave5第三層核對=([0, 3], [1, 2, 4], 否, not_a_separation)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-separation-audit · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-separation-audit；資料={"n":5,"topology":[[],[0],[0,3],[0,3,4],[0,1,3,4],[0,1,2,3,4]],"left":[0,3],"right":[1,2,4]}。請依 [left,right,valid_separation,classification] 欄序回答。
([0, 3], [1, 2, 4], 否, not_a_separation)
Wave5第三層核對=([0, 3], [1, 2, 4], 否, not_a_separation)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-separation-audit · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-separation-audit；資料={"n":5,"topology":[[],[0],[0,3],[0,3,4],[0,2,3,4],[0,1,2,3,4]],"left":[0,3],"right":[1,2,4]}。請依 [left,right,valid_separation,classification] 欄序回答。
([0, 3], [1, 2, 4], 否, not_a_separation)
Wave5第三層核對=([0, 3], [1, 2, 4], 否, not_a_separation)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-separation-audit · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-separation-audit；資料={"n":5,"topology":[[],[0],[0,4],[0,1,4],[0,1,2,4],[0,1,2,3,4]],"left":[0,4],"right":[1,2,3]}。請依 [left,right,valid_separation,classification] 欄序回答。
([0, 4], [1, 2, 3], 否, not_a_separation)
Wave5第三層核對=([0, 4], [1, 2, 3], 否, not_a_separation)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-separation-audit · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-separation-audit；資料={"n":5,"topology":[[],[0],[0,4],[0,1,4],[0,1,3,4],[0,1,2,3,4]],"left":[0,4],"right":[1,2,3]}。請依 [left,right,valid_separation,classification] 欄序回答。
([0, 4], [1, 2, 3], 否, not_a_separation)
Wave5第三層核對=([0, 4], [1, 2, 3], 否, not_a_separation)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-separation-audit · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-separation-audit；資料={"n":5,"topology":[[],[0],[0,4],[0,2,4],[0,1,2,4],[0,1,2,3,4]],"left":[0,4],"right":[1,2,3]}。請依 [left,right,valid_separation,classification] 欄序回答。
([0, 4], [1, 2, 3], 否, not_a_separation)
Wave5第三層核對=([0, 4], [1, 2, 3], 否, not_a_separation)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-separation-audit · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-separation-audit；資料={"n":5,"topology":[[],[0],[0,4],[0,2,4],[0,2,3,4],[0,1,2,3,4]],"left":[0,4],"right":[1,2,3]}。請依 [left,right,valid_separation,classification] 欄序回答。
([0, 4], [1, 2, 3], 否, not_a_separation)
Wave5第三層核對=([0, 4], [1, 2, 3], 否, not_a_separation)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-separation-audit · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-separation-audit；資料={"n":5,"topology":[[],[0],[0,4],[0,3,4],[0,1,3,4],[0,1,2,3,4]],"left":[0,4],"right":[1,2,3]}。請依 [left,right,valid_separation,classification] 欄序回答。
([0, 4], [1, 2, 3], 否, not_a_separation)
Wave5第三層核對=([0, 4], [1, 2, 3], 否, not_a_separation)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-separation-audit · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-separation-audit；資料={"n":5,"topology":[[],[0],[0,4],[0,3,4],[0,2,3,4],[0,1,2,3,4]],"left":[0,4],"right":[1,2,3]}。請依 [left,right,valid_separation,classification] 欄序回答。
([0, 4], [1, 2, 3], 否, not_a_separation)
Wave5第三層核對=([0, 4], [1, 2, 3], 否, not_a_separation)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-separation-audit · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-separation-audit；資料={"n":5,"topology":[[],[1],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4]],"left":[0,1],"right":[2,3,4]}。請依 [left,right,valid_separation,classification] 欄序回答。
([0, 1], [2, 3, 4], 否, not_a_separation)
Wave5第三層核對=([0, 1], [2, 3, 4], 否, not_a_separation)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-separation-audit · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-clopen-witness；資料={"n":5,"topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4]],"subset":[0,1]}。請依 [subset,complement,clopen,nontrivial,disconnects,certificate] 欄序回答。
([0, 1], [2, 3, 4], 否, 是, 否, nontrivial_clopen_witness)
Wave5第三層核對=([0, 1], [2, 3, 4], 否, 是, 否, nontrivial_clopen_witness)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-clopen-witness · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-clopen-witness；資料={"n":5,"topology":[[],[0],[0,1],[0,1,2],[0,1,2,4],[0,1,2,3,4]],"subset":[0,1]}。請依 [subset,complement,clopen,nontrivial,disconnects,certificate] 欄序回答。
([0, 1], [2, 3, 4], 否, 是, 否, nontrivial_clopen_witness)
Wave5第三層核對=([0, 1], [2, 3, 4], 否, 是, 否, nontrivial_clopen_witness)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-clopen-witness · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-clopen-witness；資料={"n":5,"topology":[[],[0],[0,1],[0,1,3],[0,1,2,3],[0,1,2,3,4]],"subset":[0,1]}。請依 [subset,complement,clopen,nontrivial,disconnects,certificate] 欄序回答。
([0, 1], [2, 3, 4], 否, 是, 否, nontrivial_clopen_witness)
Wave5第三層核對=([0, 1], [2, 3, 4], 否, 是, 否, nontrivial_clopen_witness)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-clopen-witness · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-clopen-witness；資料={"n":5,"topology":[[],[0],[0,1],[0,1,3],[0,1,3,4],[0,1,2,3,4]],"subset":[0,1]}。請依 [subset,complement,clopen,nontrivial,disconnects,certificate] 欄序回答。
([0, 1], [2, 3, 4], 否, 是, 否, nontrivial_clopen_witness)
Wave5第三層核對=([0, 1], [2, 3, 4], 否, 是, 否, nontrivial_clopen_witness)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-clopen-witness · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-clopen-witness；資料={"n":5,"topology":[[],[0],[0,1],[0,1,4],[0,1,2,4],[0,1,2,3,4]],"subset":[0,1]}。請依 [subset,complement,clopen,nontrivial,disconnects,certificate] 欄序回答。
([0, 1], [2, 3, 4], 否, 是, 否, nontrivial_clopen_witness)
Wave5第三層核對=([0, 1], [2, 3, 4], 否, 是, 否, nontrivial_clopen_witness)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-clopen-witness · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-clopen-witness；資料={"n":5,"topology":[[],[0],[0,1],[0,1,4],[0,1,3,4],[0,1,2,3,4]],"subset":[0,1]}。請依 [subset,complement,clopen,nontrivial,disconnects,certificate] 欄序回答。
([0, 1], [2, 3, 4], 否, 是, 否, nontrivial_clopen_witness)
Wave5第三層核對=([0, 1], [2, 3, 4], 否, 是, 否, nontrivial_clopen_witness)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-clopen-witness · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-clopen-witness；資料={"n":5,"topology":[[],[0],[0,2],[0,1,2],[0,1,2,3],[0,1,2,3,4]],"subset":[0,2]}。請依 [subset,complement,clopen,nontrivial,disconnects,certificate] 欄序回答。
([0, 2], [1, 3, 4], 否, 是, 否, nontrivial_clopen_witness)
Wave5第三層核對=([0, 2], [1, 3, 4], 否, 是, 否, nontrivial_clopen_witness)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-clopen-witness · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-clopen-witness；資料={"n":5,"topology":[[],[0],[0,2],[0,1,2],[0,1,2,4],[0,1,2,3,4]],"subset":[0,2]}。請依 [subset,complement,clopen,nontrivial,disconnects,certificate] 欄序回答。
([0, 2], [1, 3, 4], 否, 是, 否, nontrivial_clopen_witness)
Wave5第三層核對=([0, 2], [1, 3, 4], 否, 是, 否, nontrivial_clopen_witness)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-clopen-witness · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-clopen-witness；資料={"n":5,"topology":[[],[0],[0,2],[0,2,3],[0,1,2,3],[0,1,2,3,4]],"subset":[0,2]}。請依 [subset,complement,clopen,nontrivial,disconnects,certificate] 欄序回答。
([0, 2], [1, 3, 4], 否, 是, 否, nontrivial_clopen_witness)
Wave5第三層核對=([0, 2], [1, 3, 4], 否, 是, 否, nontrivial_clopen_witness)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-clopen-witness · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-clopen-witness；資料={"n":5,"topology":[[],[0],[0,2],[0,2,3],[0,2,3,4],[0,1,2,3,4]],"subset":[0,2]}。請依 [subset,complement,clopen,nontrivial,disconnects,certificate] 欄序回答。
([0, 2], [1, 3, 4], 否, 是, 否, nontrivial_clopen_witness)
Wave5第三層核對=([0, 2], [1, 3, 4], 否, 是, 否, nontrivial_clopen_witness)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-clopen-witness · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-clopen-witness；資料={"n":5,"topology":[[],[0],[0,2],[0,2,4],[0,1,2,4],[0,1,2,3,4]],"subset":[0,2]}。請依 [subset,complement,clopen,nontrivial,disconnects,certificate] 欄序回答。
([0, 2], [1, 3, 4], 否, 是, 否, nontrivial_clopen_witness)
Wave5第三層核對=([0, 2], [1, 3, 4], 否, 是, 否, nontrivial_clopen_witness)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-clopen-witness · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-clopen-witness；資料={"n":5,"topology":[[],[0],[0,2],[0,2,4],[0,2,3,4],[0,1,2,3,4]],"subset":[0,2]}。請依 [subset,complement,clopen,nontrivial,disconnects,certificate] 欄序回答。
([0, 2], [1, 3, 4], 否, 是, 否, nontrivial_clopen_witness)
Wave5第三層核對=([0, 2], [1, 3, 4], 否, 是, 否, nontrivial_clopen_witness)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-clopen-witness · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-clopen-witness；資料={"n":5,"topology":[[],[0],[0,3],[0,1,3],[0,1,2,3],[0,1,2,3,4]],"subset":[0,3]}。請依 [subset,complement,clopen,nontrivial,disconnects,certificate] 欄序回答。
([0, 3], [1, 2, 4], 否, 是, 否, nontrivial_clopen_witness)
Wave5第三層核對=([0, 3], [1, 2, 4], 否, 是, 否, nontrivial_clopen_witness)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-clopen-witness · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-clopen-witness；資料={"n":5,"topology":[[],[0],[0,3],[0,1,3],[0,1,3,4],[0,1,2,3,4]],"subset":[0,3]}。請依 [subset,complement,clopen,nontrivial,disconnects,certificate] 欄序回答。
([0, 3], [1, 2, 4], 否, 是, 否, nontrivial_clopen_witness)
Wave5第三層核對=([0, 3], [1, 2, 4], 否, 是, 否, nontrivial_clopen_witness)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-clopen-witness · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-clopen-witness；資料={"n":5,"topology":[[],[0],[0,3],[0,2,3],[0,1,2,3],[0,1,2,3,4]],"subset":[0,3]}。請依 [subset,complement,clopen,nontrivial,disconnects,certificate] 欄序回答。
([0, 3], [1, 2, 4], 否, 是, 否, nontrivial_clopen_witness)
Wave5第三層核對=([0, 3], [1, 2, 4], 否, 是, 否, nontrivial_clopen_witness)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-clopen-witness · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-clopen-witness；資料={"n":5,"topology":[[],[0],[0,3],[0,2,3],[0,2,3,4],[0,1,2,3,4]],"subset":[0,3]}。請依 [subset,complement,clopen,nontrivial,disconnects,certificate] 欄序回答。
([0, 3], [1, 2, 4], 否, 是, 否, nontrivial_clopen_witness)
Wave5第三層核對=([0, 3], [1, 2, 4], 否, 是, 否, nontrivial_clopen_witness)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-clopen-witness · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-clopen-witness；資料={"n":5,"topology":[[],[0],[0,3],[0,3,4],[0,1,3,4],[0,1,2,3,4]],"subset":[0,3]}。請依 [subset,complement,clopen,nontrivial,disconnects,certificate] 欄序回答。
([0, 3], [1, 2, 4], 否, 是, 否, nontrivial_clopen_witness)
Wave5第三層核對=([0, 3], [1, 2, 4], 否, 是, 否, nontrivial_clopen_witness)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-clopen-witness · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-clopen-witness；資料={"n":5,"topology":[[],[0],[0,3],[0,3,4],[0,2,3,4],[0,1,2,3,4]],"subset":[0,3]}。請依 [subset,complement,clopen,nontrivial,disconnects,certificate] 欄序回答。
([0, 3], [1, 2, 4], 否, 是, 否, nontrivial_clopen_witness)
Wave5第三層核對=([0, 3], [1, 2, 4], 否, 是, 否, nontrivial_clopen_witness)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-clopen-witness · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-clopen-witness；資料={"n":5,"topology":[[],[0],[0,4],[0,1,4],[0,1,2,4],[0,1,2,3,4]],"subset":[0,4]}。請依 [subset,complement,clopen,nontrivial,disconnects,certificate] 欄序回答。
([0, 4], [1, 2, 3], 否, 是, 否, nontrivial_clopen_witness)
Wave5第三層核對=([0, 4], [1, 2, 3], 否, 是, 否, nontrivial_clopen_witness)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-clopen-witness · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-clopen-witness；資料={"n":5,"topology":[[],[0],[0,4],[0,1,4],[0,1,3,4],[0,1,2,3,4]],"subset":[0,4]}。請依 [subset,complement,clopen,nontrivial,disconnects,certificate] 欄序回答。
([0, 4], [1, 2, 3], 否, 是, 否, nontrivial_clopen_witness)
Wave5第三層核對=([0, 4], [1, 2, 3], 否, 是, 否, nontrivial_clopen_witness)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-clopen-witness · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-clopen-witness；資料={"n":5,"topology":[[],[0],[0,4],[0,2,4],[0,1,2,4],[0,1,2,3,4]],"subset":[0,4]}。請依 [subset,complement,clopen,nontrivial,disconnects,certificate] 欄序回答。
([0, 4], [1, 2, 3], 否, 是, 否, nontrivial_clopen_witness)
Wave5第三層核對=([0, 4], [1, 2, 3], 否, 是, 否, nontrivial_clopen_witness)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-clopen-witness · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-clopen-witness；資料={"n":5,"topology":[[],[0],[0,4],[0,2,4],[0,2,3,4],[0,1,2,3,4]],"subset":[0,4]}。請依 [subset,complement,clopen,nontrivial,disconnects,certificate] 欄序回答。
([0, 4], [1, 2, 3], 否, 是, 否, nontrivial_clopen_witness)
Wave5第三層核對=([0, 4], [1, 2, 3], 否, 是, 否, nontrivial_clopen_witness)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-clopen-witness · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-clopen-witness；資料={"n":5,"topology":[[],[0],[0,4],[0,3,4],[0,1,3,4],[0,1,2,3,4]],"subset":[0,4]}。請依 [subset,complement,clopen,nontrivial,disconnects,certificate] 欄序回答。
([0, 4], [1, 2, 3], 否, 是, 否, nontrivial_clopen_witness)
Wave5第三層核對=([0, 4], [1, 2, 3], 否, 是, 否, nontrivial_clopen_witness)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-clopen-witness · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-clopen-witness；資料={"n":5,"topology":[[],[0],[0,4],[0,3,4],[0,2,3,4],[0,1,2,3,4]],"subset":[0,4]}。請依 [subset,complement,clopen,nontrivial,disconnects,certificate] 欄序回答。
([0, 4], [1, 2, 3], 否, 是, 否, nontrivial_clopen_witness)
Wave5第三層核對=([0, 4], [1, 2, 3], 否, 是, 否, nontrivial_clopen_witness)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-clopen-witness · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-clopen-witness；資料={"n":5,"topology":[[],[1],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4]],"subset":[0,1]}。請依 [subset,complement,clopen,nontrivial,disconnects,certificate] 欄序回答。
([0, 1], [2, 3, 4], 否, 是, 否, nontrivial_clopen_witness)
Wave5第三層核對=([0, 1], [2, 3, 4], 否, 是, 否, nontrivial_clopen_witness)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-clopen-witness · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-exhaustive；資料={"n":5,"topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4]]}。請依 [clopen_sets,nontrivial_clopen,connected,certificate] 欄序回答。
([[], [0, 1, 2, 3, 4]], [], 是, exhaustive_complete_finite_topology)
Wave5第三層核對=([[], [0, 1, 2, 3, 4]], [], 是, exhaustive_complete_finite_topology)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-exhaustive · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-exhaustive；資料={"n":5,"topology":[[],[0],[0,1],[0,1,2],[0,1,2,4],[0,1,2,3,4]]}。請依 [clopen_sets,nontrivial_clopen,connected,certificate] 欄序回答。
([[], [0, 1, 2, 3, 4]], [], 是, exhaustive_complete_finite_topology)
Wave5第三層核對=([[], [0, 1, 2, 3, 4]], [], 是, exhaustive_complete_finite_topology)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-exhaustive · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-exhaustive；資料={"n":5,"topology":[[],[0],[0,1],[0,1,3],[0,1,2,3],[0,1,2,3,4]]}。請依 [clopen_sets,nontrivial_clopen,connected,certificate] 欄序回答。
([[], [0, 1, 2, 3, 4]], [], 是, exhaustive_complete_finite_topology)
Wave5第三層核對=([[], [0, 1, 2, 3, 4]], [], 是, exhaustive_complete_finite_topology)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-exhaustive · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-exhaustive；資料={"n":5,"topology":[[],[0],[0,1],[0,1,3],[0,1,3,4],[0,1,2,3,4]]}。請依 [clopen_sets,nontrivial_clopen,connected,certificate] 欄序回答。
([[], [0, 1, 2, 3, 4]], [], 是, exhaustive_complete_finite_topology)
Wave5第三層核對=([[], [0, 1, 2, 3, 4]], [], 是, exhaustive_complete_finite_topology)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-exhaustive · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-exhaustive；資料={"n":5,"topology":[[],[0],[0,1],[0,1,4],[0,1,2,4],[0,1,2,3,4]]}。請依 [clopen_sets,nontrivial_clopen,connected,certificate] 欄序回答。
([[], [0, 1, 2, 3, 4]], [], 是, exhaustive_complete_finite_topology)
Wave5第三層核對=([[], [0, 1, 2, 3, 4]], [], 是, exhaustive_complete_finite_topology)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-exhaustive · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-exhaustive；資料={"n":5,"topology":[[],[0],[0,1],[0,1,4],[0,1,3,4],[0,1,2,3,4]]}。請依 [clopen_sets,nontrivial_clopen,connected,certificate] 欄序回答。
([[], [0, 1, 2, 3, 4]], [], 是, exhaustive_complete_finite_topology)
Wave5第三層核對=([[], [0, 1, 2, 3, 4]], [], 是, exhaustive_complete_finite_topology)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-exhaustive · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-exhaustive；資料={"n":5,"topology":[[],[0],[0,2],[0,1,2],[0,1,2,3],[0,1,2,3,4]]}。請依 [clopen_sets,nontrivial_clopen,connected,certificate] 欄序回答。
([[], [0, 1, 2, 3, 4]], [], 是, exhaustive_complete_finite_topology)
Wave5第三層核對=([[], [0, 1, 2, 3, 4]], [], 是, exhaustive_complete_finite_topology)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-exhaustive · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-exhaustive；資料={"n":5,"topology":[[],[0],[0,2],[0,1,2],[0,1,2,4],[0,1,2,3,4]]}。請依 [clopen_sets,nontrivial_clopen,connected,certificate] 欄序回答。
([[], [0, 1, 2, 3, 4]], [], 是, exhaustive_complete_finite_topology)
Wave5第三層核對=([[], [0, 1, 2, 3, 4]], [], 是, exhaustive_complete_finite_topology)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-exhaustive · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-exhaustive；資料={"n":5,"topology":[[],[0],[0,2],[0,2,3],[0,1,2,3],[0,1,2,3,4]]}。請依 [clopen_sets,nontrivial_clopen,connected,certificate] 欄序回答。
([[], [0, 1, 2, 3, 4]], [], 是, exhaustive_complete_finite_topology)
Wave5第三層核對=([[], [0, 1, 2, 3, 4]], [], 是, exhaustive_complete_finite_topology)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-exhaustive · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-exhaustive；資料={"n":5,"topology":[[],[0],[0,2],[0,2,3],[0,2,3,4],[0,1,2,3,4]]}。請依 [clopen_sets,nontrivial_clopen,connected,certificate] 欄序回答。
([[], [0, 1, 2, 3, 4]], [], 是, exhaustive_complete_finite_topology)
Wave5第三層核對=([[], [0, 1, 2, 3, 4]], [], 是, exhaustive_complete_finite_topology)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-exhaustive · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-exhaustive；資料={"n":5,"topology":[[],[0],[0,2],[0,2,4],[0,1,2,4],[0,1,2,3,4]]}。請依 [clopen_sets,nontrivial_clopen,connected,certificate] 欄序回答。
([[], [0, 1, 2, 3, 4]], [], 是, exhaustive_complete_finite_topology)
Wave5第三層核對=([[], [0, 1, 2, 3, 4]], [], 是, exhaustive_complete_finite_topology)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-exhaustive · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-exhaustive；資料={"n":5,"topology":[[],[0],[0,2],[0,2,4],[0,2,3,4],[0,1,2,3,4]]}。請依 [clopen_sets,nontrivial_clopen,connected,certificate] 欄序回答。
([[], [0, 1, 2, 3, 4]], [], 是, exhaustive_complete_finite_topology)
Wave5第三層核對=([[], [0, 1, 2, 3, 4]], [], 是, exhaustive_complete_finite_topology)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-exhaustive · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-exhaustive；資料={"n":5,"topology":[[],[0],[0,3],[0,1,3],[0,1,2,3],[0,1,2,3,4]]}。請依 [clopen_sets,nontrivial_clopen,connected,certificate] 欄序回答。
([[], [0, 1, 2, 3, 4]], [], 是, exhaustive_complete_finite_topology)
Wave5第三層核對=([[], [0, 1, 2, 3, 4]], [], 是, exhaustive_complete_finite_topology)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-exhaustive · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-exhaustive；資料={"n":5,"topology":[[],[0],[0,3],[0,1,3],[0,1,3,4],[0,1,2,3,4]]}。請依 [clopen_sets,nontrivial_clopen,connected,certificate] 欄序回答。
([[], [0, 1, 2, 3, 4]], [], 是, exhaustive_complete_finite_topology)
Wave5第三層核對=([[], [0, 1, 2, 3, 4]], [], 是, exhaustive_complete_finite_topology)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-exhaustive · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-exhaustive；資料={"n":5,"topology":[[],[0],[0,3],[0,2,3],[0,1,2,3],[0,1,2,3,4]]}。請依 [clopen_sets,nontrivial_clopen,connected,certificate] 欄序回答。
([[], [0, 1, 2, 3, 4]], [], 是, exhaustive_complete_finite_topology)
Wave5第三層核對=([[], [0, 1, 2, 3, 4]], [], 是, exhaustive_complete_finite_topology)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-exhaustive · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-exhaustive；資料={"n":5,"topology":[[],[0],[0,3],[0,2,3],[0,2,3,4],[0,1,2,3,4]]}。請依 [clopen_sets,nontrivial_clopen,connected,certificate] 欄序回答。
([[], [0, 1, 2, 3, 4]], [], 是, exhaustive_complete_finite_topology)
Wave5第三層核對=([[], [0, 1, 2, 3, 4]], [], 是, exhaustive_complete_finite_topology)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-exhaustive · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-exhaustive；資料={"n":5,"topology":[[],[0],[0,3],[0,3,4],[0,1,3,4],[0,1,2,3,4]]}。請依 [clopen_sets,nontrivial_clopen,connected,certificate] 欄序回答。
([[], [0, 1, 2, 3, 4]], [], 是, exhaustive_complete_finite_topology)
Wave5第三層核對=([[], [0, 1, 2, 3, 4]], [], 是, exhaustive_complete_finite_topology)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-exhaustive · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-exhaustive；資料={"n":5,"topology":[[],[0],[0,3],[0,3,4],[0,2,3,4],[0,1,2,3,4]]}。請依 [clopen_sets,nontrivial_clopen,connected,certificate] 欄序回答。
([[], [0, 1, 2, 3, 4]], [], 是, exhaustive_complete_finite_topology)
Wave5第三層核對=([[], [0, 1, 2, 3, 4]], [], 是, exhaustive_complete_finite_topology)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-exhaustive · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-exhaustive；資料={"n":5,"topology":[[],[0],[0,4],[0,1,4],[0,1,2,4],[0,1,2,3,4]]}。請依 [clopen_sets,nontrivial_clopen,connected,certificate] 欄序回答。
([[], [0, 1, 2, 3, 4]], [], 是, exhaustive_complete_finite_topology)
Wave5第三層核對=([[], [0, 1, 2, 3, 4]], [], 是, exhaustive_complete_finite_topology)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-exhaustive · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-exhaustive；資料={"n":5,"topology":[[],[0],[0,4],[0,1,4],[0,1,3,4],[0,1,2,3,4]]}。請依 [clopen_sets,nontrivial_clopen,connected,certificate] 欄序回答。
([[], [0, 1, 2, 3, 4]], [], 是, exhaustive_complete_finite_topology)
Wave5第三層核對=([[], [0, 1, 2, 3, 4]], [], 是, exhaustive_complete_finite_topology)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-exhaustive · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-exhaustive；資料={"n":5,"topology":[[],[0],[0,4],[0,2,4],[0,1,2,4],[0,1,2,3,4]]}。請依 [clopen_sets,nontrivial_clopen,connected,certificate] 欄序回答。
([[], [0, 1, 2, 3, 4]], [], 是, exhaustive_complete_finite_topology)
Wave5第三層核對=([[], [0, 1, 2, 3, 4]], [], 是, exhaustive_complete_finite_topology)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-exhaustive · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-exhaustive；資料={"n":5,"topology":[[],[0],[0,4],[0,2,4],[0,2,3,4],[0,1,2,3,4]]}。請依 [clopen_sets,nontrivial_clopen,connected,certificate] 欄序回答。
([[], [0, 1, 2, 3, 4]], [], 是, exhaustive_complete_finite_topology)
Wave5第三層核對=([[], [0, 1, 2, 3, 4]], [], 是, exhaustive_complete_finite_topology)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-exhaustive · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-exhaustive；資料={"n":5,"topology":[[],[0],[0,4],[0,3,4],[0,1,3,4],[0,1,2,3,4]]}。請依 [clopen_sets,nontrivial_clopen,connected,certificate] 欄序回答。
([[], [0, 1, 2, 3, 4]], [], 是, exhaustive_complete_finite_topology)
Wave5第三層核對=([[], [0, 1, 2, 3, 4]], [], 是, exhaustive_complete_finite_topology)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-exhaustive · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-exhaustive；資料={"n":5,"topology":[[],[0],[0,4],[0,3,4],[0,2,3,4],[0,1,2,3,4]]}。請依 [clopen_sets,nontrivial_clopen,connected,certificate] 欄序回答。
([[], [0, 1, 2, 3, 4]], [], 是, exhaustive_complete_finite_topology)
Wave5第三層核對=([[], [0, 1, 2, 3, 4]], [], 是, exhaustive_complete_finite_topology)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-exhaustive · candidate
完整有限拓撲與全部clopen/separation候選。操作=connected-exhaustive；資料={"n":5,"topology":[[],[1],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4]]}。請依 [clopen_sets,nontrivial_clopen,connected,certificate] 欄序回答。
([[], [0, 1, 2, 3, 4]], [], 是, exhaustive_complete_finite_topology)
Wave5第三層核對=([[], [0, 1, 2, 3, 4]], [], 是, exhaustive_complete_finite_topology)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示。
連通拓撲空間 · qf-mod34-connected-exhaustive · candidate
完整有限拓撲與全部clopen/separation候選；which僅指定獨立的空或單點參考慣例；n與topology描述實際待判定空間，不聲稱實際載體就是參考空間。操作=connected-empty-singleton-boundary；資料={"n":5,"topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4]],"which":"empty"}。請依 [reference_kind,actual_carrier_size,actual_connected,reference_convention] 欄序回答。
(empty, 5, 是, empty_space_connected_by_declared_vacuous_convention)
Wave5第三層核對=(empty, 5, 是, empty_space_connected_by_declared_vacuous_convention)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示；actual_connected只由實際完整拓撲決定；reference_convention不得當成該空間的連通性證書。
連通拓撲空間 · qf-mod34-connected-empty-singleton-boundary · candidate
完整有限拓撲與全部clopen/separation候選；which僅指定獨立的空或單點參考慣例；n與topology描述實際待判定空間，不聲稱實際載體就是參考空間。操作=connected-empty-singleton-boundary；資料={"n":5,"topology":[[],[0],[0,1],[0,1,2],[0,1,2,4],[0,1,2,3,4]],"which":"singleton"}。請依 [reference_kind,actual_carrier_size,actual_connected,reference_convention] 欄序回答。
(singleton, 5, 是, singleton_connected)
Wave5第三層核對=(singleton, 5, 是, singleton_connected)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示；actual_connected只由實際完整拓撲決定；reference_convention不得當成該空間的連通性證書。
連通拓撲空間 · qf-mod34-connected-empty-singleton-boundary · candidate
完整有限拓撲與全部clopen/separation候選；which僅指定獨立的空或單點參考慣例；n與topology描述實際待判定空間，不聲稱實際載體就是參考空間。操作=connected-empty-singleton-boundary；資料={"n":5,"topology":[[],[0],[0,1],[0,1,3],[0,1,2,3],[0,1,2,3,4]],"which":"empty"}。請依 [reference_kind,actual_carrier_size,actual_connected,reference_convention] 欄序回答。
(empty, 5, 是, empty_space_connected_by_declared_vacuous_convention)
Wave5第三層核對=(empty, 5, 是, empty_space_connected_by_declared_vacuous_convention)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示；actual_connected只由實際完整拓撲決定；reference_convention不得當成該空間的連通性證書。
連通拓撲空間 · qf-mod34-connected-empty-singleton-boundary · candidate
完整有限拓撲與全部clopen/separation候選；which僅指定獨立的空或單點參考慣例；n與topology描述實際待判定空間，不聲稱實際載體就是參考空間。操作=connected-empty-singleton-boundary；資料={"n":5,"topology":[[],[0],[0,1],[0,1,3],[0,1,3,4],[0,1,2,3,4]],"which":"singleton"}。請依 [reference_kind,actual_carrier_size,actual_connected,reference_convention] 欄序回答。
(singleton, 5, 是, singleton_connected)
Wave5第三層核對=(singleton, 5, 是, singleton_connected)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示；actual_connected只由實際完整拓撲決定；reference_convention不得當成該空間的連通性證書。
連通拓撲空間 · qf-mod34-connected-empty-singleton-boundary · candidate
完整有限拓撲與全部clopen/separation候選；which僅指定獨立的空或單點參考慣例；n與topology描述實際待判定空間，不聲稱實際載體就是參考空間。操作=connected-empty-singleton-boundary；資料={"n":5,"topology":[[],[0],[0,1],[0,1,4],[0,1,2,4],[0,1,2,3,4]],"which":"empty"}。請依 [reference_kind,actual_carrier_size,actual_connected,reference_convention] 欄序回答。
(empty, 5, 是, empty_space_connected_by_declared_vacuous_convention)
Wave5第三層核對=(empty, 5, 是, empty_space_connected_by_declared_vacuous_convention)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示；actual_connected只由實際完整拓撲決定；reference_convention不得當成該空間的連通性證書。
連通拓撲空間 · qf-mod34-connected-empty-singleton-boundary · candidate
完整有限拓撲與全部clopen/separation候選；which僅指定獨立的空或單點參考慣例；n與topology描述實際待判定空間，不聲稱實際載體就是參考空間。操作=connected-empty-singleton-boundary；資料={"n":5,"topology":[[],[0],[0,1],[0,1,4],[0,1,3,4],[0,1,2,3,4]],"which":"singleton"}。請依 [reference_kind,actual_carrier_size,actual_connected,reference_convention] 欄序回答。
(singleton, 5, 是, singleton_connected)
Wave5第三層核對=(singleton, 5, 是, singleton_connected)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示；actual_connected只由實際完整拓撲決定；reference_convention不得當成該空間的連通性證書。
連通拓撲空間 · qf-mod34-connected-empty-singleton-boundary · candidate
完整有限拓撲與全部clopen/separation候選；which僅指定獨立的空或單點參考慣例；n與topology描述實際待判定空間，不聲稱實際載體就是參考空間。操作=connected-empty-singleton-boundary；資料={"n":5,"topology":[[],[0],[0,2],[0,1,2],[0,1,2,3],[0,1,2,3,4]],"which":"empty"}。請依 [reference_kind,actual_carrier_size,actual_connected,reference_convention] 欄序回答。
(empty, 5, 是, empty_space_connected_by_declared_vacuous_convention)
Wave5第三層核對=(empty, 5, 是, empty_space_connected_by_declared_vacuous_convention)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示；actual_connected只由實際完整拓撲決定；reference_convention不得當成該空間的連通性證書。
連通拓撲空間 · qf-mod34-connected-empty-singleton-boundary · candidate
完整有限拓撲與全部clopen/separation候選；which僅指定獨立的空或單點參考慣例；n與topology描述實際待判定空間，不聲稱實際載體就是參考空間。操作=connected-empty-singleton-boundary；資料={"n":5,"topology":[[],[0],[0,2],[0,1,2],[0,1,2,4],[0,1,2,3,4]],"which":"singleton"}。請依 [reference_kind,actual_carrier_size,actual_connected,reference_convention] 欄序回答。
(singleton, 5, 是, singleton_connected)
Wave5第三層核對=(singleton, 5, 是, singleton_connected)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示；actual_connected只由實際完整拓撲決定；reference_convention不得當成該空間的連通性證書。
連通拓撲空間 · qf-mod34-connected-empty-singleton-boundary · candidate
完整有限拓撲與全部clopen/separation候選；which僅指定獨立的空或單點參考慣例；n與topology描述實際待判定空間，不聲稱實際載體就是參考空間。操作=connected-empty-singleton-boundary；資料={"n":5,"topology":[[],[0],[0,2],[0,2,3],[0,1,2,3],[0,1,2,3,4]],"which":"empty"}。請依 [reference_kind,actual_carrier_size,actual_connected,reference_convention] 欄序回答。
(empty, 5, 是, empty_space_connected_by_declared_vacuous_convention)
Wave5第三層核對=(empty, 5, 是, empty_space_connected_by_declared_vacuous_convention)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示；actual_connected只由實際完整拓撲決定；reference_convention不得當成該空間的連通性證書。
連通拓撲空間 · qf-mod34-connected-empty-singleton-boundary · candidate
完整有限拓撲與全部clopen/separation候選；which僅指定獨立的空或單點參考慣例；n與topology描述實際待判定空間，不聲稱實際載體就是參考空間。操作=connected-empty-singleton-boundary；資料={"n":5,"topology":[[],[0],[0,2],[0,2,3],[0,2,3,4],[0,1,2,3,4]],"which":"singleton"}。請依 [reference_kind,actual_carrier_size,actual_connected,reference_convention] 欄序回答。
(singleton, 5, 是, singleton_connected)
Wave5第三層核對=(singleton, 5, 是, singleton_connected)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示；actual_connected只由實際完整拓撲決定；reference_convention不得當成該空間的連通性證書。
連通拓撲空間 · qf-mod34-connected-empty-singleton-boundary · candidate
完整有限拓撲與全部clopen/separation候選；which僅指定獨立的空或單點參考慣例；n與topology描述實際待判定空間，不聲稱實際載體就是參考空間。操作=connected-empty-singleton-boundary；資料={"n":5,"topology":[[],[0],[0,2],[0,2,4],[0,1,2,4],[0,1,2,3,4]],"which":"empty"}。請依 [reference_kind,actual_carrier_size,actual_connected,reference_convention] 欄序回答。
(empty, 5, 是, empty_space_connected_by_declared_vacuous_convention)
Wave5第三層核對=(empty, 5, 是, empty_space_connected_by_declared_vacuous_convention)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示；actual_connected只由實際完整拓撲決定；reference_convention不得當成該空間的連通性證書。
連通拓撲空間 · qf-mod34-connected-empty-singleton-boundary · candidate
完整有限拓撲與全部clopen/separation候選；which僅指定獨立的空或單點參考慣例；n與topology描述實際待判定空間，不聲稱實際載體就是參考空間。操作=connected-empty-singleton-boundary；資料={"n":5,"topology":[[],[0],[0,2],[0,2,4],[0,2,3,4],[0,1,2,3,4]],"which":"singleton"}。請依 [reference_kind,actual_carrier_size,actual_connected,reference_convention] 欄序回答。
(singleton, 5, 是, singleton_connected)
Wave5第三層核對=(singleton, 5, 是, singleton_connected)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示；actual_connected只由實際完整拓撲決定；reference_convention不得當成該空間的連通性證書。
連通拓撲空間 · qf-mod34-connected-empty-singleton-boundary · candidate
完整有限拓撲與全部clopen/separation候選；which僅指定獨立的空或單點參考慣例；n與topology描述實際待判定空間，不聲稱實際載體就是參考空間。操作=connected-empty-singleton-boundary；資料={"n":5,"topology":[[],[0],[0,3],[0,1,3],[0,1,2,3],[0,1,2,3,4]],"which":"empty"}。請依 [reference_kind,actual_carrier_size,actual_connected,reference_convention] 欄序回答。
(empty, 5, 是, empty_space_connected_by_declared_vacuous_convention)
Wave5第三層核對=(empty, 5, 是, empty_space_connected_by_declared_vacuous_convention)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示；actual_connected只由實際完整拓撲決定；reference_convention不得當成該空間的連通性證書。
連通拓撲空間 · qf-mod34-connected-empty-singleton-boundary · candidate
完整有限拓撲與全部clopen/separation候選；which僅指定獨立的空或單點參考慣例；n與topology描述實際待判定空間，不聲稱實際載體就是參考空間。操作=connected-empty-singleton-boundary；資料={"n":5,"topology":[[],[0],[0,3],[0,1,3],[0,1,3,4],[0,1,2,3,4]],"which":"singleton"}。請依 [reference_kind,actual_carrier_size,actual_connected,reference_convention] 欄序回答。
(singleton, 5, 是, singleton_connected)
Wave5第三層核對=(singleton, 5, 是, singleton_connected)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示；actual_connected只由實際完整拓撲決定；reference_convention不得當成該空間的連通性證書。
連通拓撲空間 · qf-mod34-connected-empty-singleton-boundary · candidate
完整有限拓撲與全部clopen/separation候選；which僅指定獨立的空或單點參考慣例；n與topology描述實際待判定空間，不聲稱實際載體就是參考空間。操作=connected-empty-singleton-boundary；資料={"n":5,"topology":[[],[0],[0,3],[0,2,3],[0,1,2,3],[0,1,2,3,4]],"which":"empty"}。請依 [reference_kind,actual_carrier_size,actual_connected,reference_convention] 欄序回答。
(empty, 5, 是, empty_space_connected_by_declared_vacuous_convention)
Wave5第三層核對=(empty, 5, 是, empty_space_connected_by_declared_vacuous_convention)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示；actual_connected只由實際完整拓撲決定；reference_convention不得當成該空間的連通性證書。
連通拓撲空間 · qf-mod34-connected-empty-singleton-boundary · candidate
完整有限拓撲與全部clopen/separation候選；which僅指定獨立的空或單點參考慣例；n與topology描述實際待判定空間，不聲稱實際載體就是參考空間。操作=connected-empty-singleton-boundary；資料={"n":5,"topology":[[],[0],[0,3],[0,2,3],[0,2,3,4],[0,1,2,3,4]],"which":"singleton"}。請依 [reference_kind,actual_carrier_size,actual_connected,reference_convention] 欄序回答。
(singleton, 5, 是, singleton_connected)
Wave5第三層核對=(singleton, 5, 是, singleton_connected)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示；actual_connected只由實際完整拓撲決定；reference_convention不得當成該空間的連通性證書。
連通拓撲空間 · qf-mod34-connected-empty-singleton-boundary · candidate
完整有限拓撲與全部clopen/separation候選；which僅指定獨立的空或單點參考慣例；n與topology描述實際待判定空間，不聲稱實際載體就是參考空間。操作=connected-empty-singleton-boundary；資料={"n":5,"topology":[[],[0],[0,3],[0,3,4],[0,1,3,4],[0,1,2,3,4]],"which":"empty"}。請依 [reference_kind,actual_carrier_size,actual_connected,reference_convention] 欄序回答。
(empty, 5, 是, empty_space_connected_by_declared_vacuous_convention)
Wave5第三層核對=(empty, 5, 是, empty_space_connected_by_declared_vacuous_convention)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示；actual_connected只由實際完整拓撲決定；reference_convention不得當成該空間的連通性證書。
連通拓撲空間 · qf-mod34-connected-empty-singleton-boundary · candidate
完整有限拓撲與全部clopen/separation候選；which僅指定獨立的空或單點參考慣例；n與topology描述實際待判定空間，不聲稱實際載體就是參考空間。操作=connected-empty-singleton-boundary；資料={"n":5,"topology":[[],[0],[0,3],[0,3,4],[0,2,3,4],[0,1,2,3,4]],"which":"singleton"}。請依 [reference_kind,actual_carrier_size,actual_connected,reference_convention] 欄序回答。
(singleton, 5, 是, singleton_connected)
Wave5第三層核對=(singleton, 5, 是, singleton_connected)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示；actual_connected只由實際完整拓撲決定；reference_convention不得當成該空間的連通性證書。
連通拓撲空間 · qf-mod34-connected-empty-singleton-boundary · candidate
完整有限拓撲與全部clopen/separation候選；which僅指定獨立的空或單點參考慣例；n與topology描述實際待判定空間，不聲稱實際載體就是參考空間。操作=connected-empty-singleton-boundary；資料={"n":5,"topology":[[],[0],[0,4],[0,1,4],[0,1,2,4],[0,1,2,3,4]],"which":"empty"}。請依 [reference_kind,actual_carrier_size,actual_connected,reference_convention] 欄序回答。
(empty, 5, 是, empty_space_connected_by_declared_vacuous_convention)
Wave5第三層核對=(empty, 5, 是, empty_space_connected_by_declared_vacuous_convention)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示；actual_connected只由實際完整拓撲決定；reference_convention不得當成該空間的連通性證書。
連通拓撲空間 · qf-mod34-connected-empty-singleton-boundary · candidate
完整有限拓撲與全部clopen/separation候選；which僅指定獨立的空或單點參考慣例；n與topology描述實際待判定空間，不聲稱實際載體就是參考空間。操作=connected-empty-singleton-boundary；資料={"n":5,"topology":[[],[0],[0,4],[0,1,4],[0,1,3,4],[0,1,2,3,4]],"which":"singleton"}。請依 [reference_kind,actual_carrier_size,actual_connected,reference_convention] 欄序回答。
(singleton, 5, 是, singleton_connected)
Wave5第三層核對=(singleton, 5, 是, singleton_connected)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示；actual_connected只由實際完整拓撲決定；reference_convention不得當成該空間的連通性證書。
連通拓撲空間 · qf-mod34-connected-empty-singleton-boundary · candidate
完整有限拓撲與全部clopen/separation候選；which僅指定獨立的空或單點參考慣例；n與topology描述實際待判定空間，不聲稱實際載體就是參考空間。操作=connected-empty-singleton-boundary；資料={"n":5,"topology":[[],[0],[0,4],[0,2,4],[0,1,2,4],[0,1,2,3,4]],"which":"empty"}。請依 [reference_kind,actual_carrier_size,actual_connected,reference_convention] 欄序回答。
(empty, 5, 是, empty_space_connected_by_declared_vacuous_convention)
Wave5第三層核對=(empty, 5, 是, empty_space_connected_by_declared_vacuous_convention)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示；actual_connected只由實際完整拓撲決定；reference_convention不得當成該空間的連通性證書。
連通拓撲空間 · qf-mod34-connected-empty-singleton-boundary · candidate
完整有限拓撲與全部clopen/separation候選；which僅指定獨立的空或單點參考慣例；n與topology描述實際待判定空間，不聲稱實際載體就是參考空間。操作=connected-empty-singleton-boundary；資料={"n":5,"topology":[[],[0],[0,4],[0,2,4],[0,2,3,4],[0,1,2,3,4]],"which":"singleton"}。請依 [reference_kind,actual_carrier_size,actual_connected,reference_convention] 欄序回答。
(singleton, 5, 是, singleton_connected)
Wave5第三層核對=(singleton, 5, 是, singleton_connected)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示；actual_connected只由實際完整拓撲決定；reference_convention不得當成該空間的連通性證書。
連通拓撲空間 · qf-mod34-connected-empty-singleton-boundary · candidate
完整有限拓撲與全部clopen/separation候選；which僅指定獨立的空或單點參考慣例；n與topology描述實際待判定空間，不聲稱實際載體就是參考空間。操作=connected-empty-singleton-boundary；資料={"n":5,"topology":[[],[0],[0,4],[0,3,4],[0,1,3,4],[0,1,2,3,4]],"which":"empty"}。請依 [reference_kind,actual_carrier_size,actual_connected,reference_convention] 欄序回答。
(empty, 5, 是, empty_space_connected_by_declared_vacuous_convention)
Wave5第三層核對=(empty, 5, 是, empty_space_connected_by_declared_vacuous_convention)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示；actual_connected只由實際完整拓撲決定；reference_convention不得當成該空間的連通性證書。
連通拓撲空間 · qf-mod34-connected-empty-singleton-boundary · candidate
完整有限拓撲與全部clopen/separation候選；which僅指定獨立的空或單點參考慣例；n與topology描述實際待判定空間，不聲稱實際載體就是參考空間。操作=connected-empty-singleton-boundary；資料={"n":5,"topology":[[],[0],[0,4],[0,3,4],[0,2,3,4],[0,1,2,3,4]],"which":"singleton"}。請依 [reference_kind,actual_carrier_size,actual_connected,reference_convention] 欄序回答。
(singleton, 5, 是, singleton_connected)
Wave5第三層核對=(singleton, 5, 是, singleton_connected)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示；actual_connected只由實際完整拓撲決定；reference_convention不得當成該空間的連通性證書。
連通拓撲空間 · qf-mod34-connected-empty-singleton-boundary · candidate
完整有限拓撲與全部clopen/separation候選；which僅指定獨立的空或單點參考慣例；n與topology描述實際待判定空間，不聲稱實際載體就是參考空間。操作=connected-empty-singleton-boundary；資料={"n":5,"topology":[[],[1],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4]],"which":"empty"}。請依 [reference_kind,actual_carrier_size,actual_connected,reference_convention] 欄序回答。
(empty, 5, 是, empty_space_connected_by_declared_vacuous_convention)
Wave5第三層核對=(empty, 5, 是, empty_space_connected_by_declared_vacuous_convention)；依完整明示資料重算；connected需exhaustive排除非平凡clopen且disconnected需witness；不混同graph connectivity；空空間慣例與singleton界線明示；actual_connected只由實際完整拓撲決定；reference_convention不得當成該空間的連通性證書。
連通拓撲空間 · qf-mod34-connected-empty-singleton-boundary · candidate