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拓撲連通分支基礎 · 脈衝 R07
本批已通過 Schema、去重、來源快照與獨立答案重算；仍未標記為人工審定。
本題庫已有對應的中英逐步詳解。原題的 candidate 與英文 ai_candidate 狀態保留；AI 覆核、有限計算與 Lean 形式證明分開標示。
batch-20261015-advance-20261117-r07-topological-connected-component-foundations · 2026-10-15 · 100 題
欄序為來源綁定的呈現補充；原始 JSONL 與數學答案不變。
欄序與來源綁定資料
1. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-connected-subsets；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,1],[2,3,4,5]],"basepoint":0}。請依 [basepoint, all_containing_connected_subsets, their_union, union_connected, certificate] 欄序回答。
查看答案與解釋
(0, [[0], [0, 1]], [0, 1], 是, union_of_connected_subsets_sharing_basepoint_is_connected)
Wave6第十一層核對=(0, [[0], [0, 1]], [0, 1], 是, union_of_connected_subsets_sharing_basepoint_is_connected)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-connected-subsets · candidate
2. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-connected-subsets；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,2],[1,3,4,5]],"basepoint":0}。請依 [basepoint, all_containing_connected_subsets, their_union, union_connected, certificate] 欄序回答。
查看答案與解釋
(0, [[0], [0, 2]], [0, 2], 是, union_of_connected_subsets_sharing_basepoint_is_connected)
Wave6第十一層核對=(0, [[0], [0, 2]], [0, 2], 是, union_of_connected_subsets_sharing_basepoint_is_connected)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-connected-subsets · candidate
3. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-connected-subsets；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,1,2],[3,4,5]],"basepoint":0}。請依 [basepoint, all_containing_connected_subsets, their_union, union_connected, certificate] 欄序回答。
查看答案與解釋
(0, [[0], [0, 1], [0, 2], [0, 1, 2]], [0, 1, 2], 是, union_of_connected_subsets_sharing_basepoint_is_connected)
Wave6第十一層核對=(0, [[0], [0, 1], [0, 2], [0, 1, 2]], [0, 1, 2], 是, union_of_connected_subsets_sharing_basepoint_is_connected)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-connected-subsets · candidate
4. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-connected-subsets；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,3],[1,2,4,5]],"basepoint":0}。請依 [basepoint, all_containing_connected_subsets, their_union, union_connected, certificate] 欄序回答。
查看答案與解釋
(0, [[0], [0, 3]], [0, 3], 是, union_of_connected_subsets_sharing_basepoint_is_connected)
Wave6第十一層核對=(0, [[0], [0, 3]], [0, 3], 是, union_of_connected_subsets_sharing_basepoint_is_connected)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-connected-subsets · candidate
5. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-connected-subsets；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,1,3],[2,4,5]],"basepoint":0}。請依 [basepoint, all_containing_connected_subsets, their_union, union_connected, certificate] 欄序回答。
查看答案與解釋
(0, [[0], [0, 1], [0, 3], [0, 1, 3]], [0, 1, 3], 是, union_of_connected_subsets_sharing_basepoint_is_connected)
Wave6第十一層核對=(0, [[0], [0, 1], [0, 3], [0, 1, 3]], [0, 1, 3], 是, union_of_connected_subsets_sharing_basepoint_is_connected)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-connected-subsets · candidate
6. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-connected-subsets；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,2,3],[1,4,5]],"basepoint":0}。請依 [basepoint, all_containing_connected_subsets, their_union, union_connected, certificate] 欄序回答。
查看答案與解釋
(0, [[0], [0, 2], [0, 3], [0, 2, 3]], [0, 2, 3], 是, union_of_connected_subsets_sharing_basepoint_is_connected)
Wave6第十一層核對=(0, [[0], [0, 2], [0, 3], [0, 2, 3]], [0, 2, 3], 是, union_of_connected_subsets_sharing_basepoint_is_connected)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-connected-subsets · candidate
7. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-connected-subsets；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,1,2,3],[4,5]],"basepoint":0}。請依 [basepoint, all_containing_connected_subsets, their_union, union_connected, certificate] 欄序回答。
查看答案與解釋
(0, [[0], [0, 1], [0, 2], [0, 1, 2], [0, 3], [0, 1, 3], [0, 2, 3], [0, 1, 2, 3]], [0, 1, 2, 3], 是, union_of_connected_subsets_sharing_basepoint_is_connected)
Wave6第十一層核對=(0, [[0], [0, 1], [0, 2], [0, 1, 2], [0, 3], [0, 1, 3], [0, 2, 3], [0, 1, 2, 3]], [0, 1, 2, 3], 是, union_of_connected_subsets_sharing_basepoint_is_connected)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-connected-subsets · candidate
8. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-connected-subsets；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,4],[1,2,3,5]],"basepoint":0}。請依 [basepoint, all_containing_connected_subsets, their_union, union_connected, certificate] 欄序回答。
查看答案與解釋
(0, [[0], [0, 4]], [0, 4], 是, union_of_connected_subsets_sharing_basepoint_is_connected)
Wave6第十一層核對=(0, [[0], [0, 4]], [0, 4], 是, union_of_connected_subsets_sharing_basepoint_is_connected)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-connected-subsets · candidate
9. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-connected-subsets；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,1,4],[2,3,5]],"basepoint":0}。請依 [basepoint, all_containing_connected_subsets, their_union, union_connected, certificate] 欄序回答。
查看答案與解釋
(0, [[0], [0, 1], [0, 4], [0, 1, 4]], [0, 1, 4], 是, union_of_connected_subsets_sharing_basepoint_is_connected)
Wave6第十一層核對=(0, [[0], [0, 1], [0, 4], [0, 1, 4]], [0, 1, 4], 是, union_of_connected_subsets_sharing_basepoint_is_connected)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-connected-subsets · candidate
10. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-connected-subsets；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,2,4],[1,3,5]],"basepoint":0}。請依 [basepoint, all_containing_connected_subsets, their_union, union_connected, certificate] 欄序回答。
查看答案與解釋
(0, [[0], [0, 2], [0, 4], [0, 2, 4]], [0, 2, 4], 是, union_of_connected_subsets_sharing_basepoint_is_connected)
Wave6第十一層核對=(0, [[0], [0, 2], [0, 4], [0, 2, 4]], [0, 2, 4], 是, union_of_connected_subsets_sharing_basepoint_is_connected)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-connected-subsets · candidate
11. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-connected-subsets；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,1,2,4],[3,5]],"basepoint":0}。請依 [basepoint, all_containing_connected_subsets, their_union, union_connected, certificate] 欄序回答。
查看答案與解釋
(0, [[0], [0, 1], [0, 2], [0, 1, 2], [0, 4], [0, 1, 4], [0, 2, 4], [0, 1, 2, 4]], [0, 1, 2, 4], 是, union_of_connected_subsets_sharing_basepoint_is_connected)
Wave6第十一層核對=(0, [[0], [0, 1], [0, 2], [0, 1, 2], [0, 4], [0, 1, 4], [0, 2, 4], [0, 1, 2, 4]], [0, 1, 2, 4], 是, union_of_connected_subsets_sharing_basepoint_is_connected)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-connected-subsets · candidate
12. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-connected-subsets；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,3,4],[1,2,5]],"basepoint":0}。請依 [basepoint, all_containing_connected_subsets, their_union, union_connected, certificate] 欄序回答。
查看答案與解釋
(0, [[0], [0, 3], [0, 4], [0, 3, 4]], [0, 3, 4], 是, union_of_connected_subsets_sharing_basepoint_is_connected)
Wave6第十一層核對=(0, [[0], [0, 3], [0, 4], [0, 3, 4]], [0, 3, 4], 是, union_of_connected_subsets_sharing_basepoint_is_connected)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-connected-subsets · candidate
13. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-connected-subsets；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,1,3,4],[2,5]],"basepoint":0}。請依 [basepoint, all_containing_connected_subsets, their_union, union_connected, certificate] 欄序回答。
查看答案與解釋
(0, [[0], [0, 1], [0, 3], [0, 1, 3], [0, 4], [0, 1, 4], [0, 3, 4], [0, 1, 3, 4]], [0, 1, 3, 4], 是, union_of_connected_subsets_sharing_basepoint_is_connected)
Wave6第十一層核對=(0, [[0], [0, 1], [0, 3], [0, 1, 3], [0, 4], [0, 1, 4], [0, 3, 4], [0, 1, 3, 4]], [0, 1, 3, 4], 是, union_of_connected_subsets_sharing_basepoint_is_connected)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-connected-subsets · candidate
14. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-connected-subsets；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,2,3,4],[1,5]],"basepoint":0}。請依 [basepoint, all_containing_connected_subsets, their_union, union_connected, certificate] 欄序回答。
查看答案與解釋
(0, [[0], [0, 2], [0, 3], [0, 2, 3], [0, 4], [0, 2, 4], [0, 3, 4], [0, 2, 3, 4]], [0, 2, 3, 4], 是, union_of_connected_subsets_sharing_basepoint_is_connected)
Wave6第十一層核對=(0, [[0], [0, 2], [0, 3], [0, 2, 3], [0, 4], [0, 2, 4], [0, 3, 4], [0, 2, 3, 4]], [0, 2, 3, 4], 是, union_of_connected_subsets_sharing_basepoint_is_connected)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-connected-subsets · candidate
15. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-connected-subsets；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,1,2,3,4],[5]],"basepoint":0}。請依 [basepoint, all_containing_connected_subsets, their_union, union_connected, certificate] 欄序回答。
查看答案與解釋
(0, [[0], [0, 1], [0, 2], [0, 1, 2], [0, 3], [0, 1, 3], [0, 2, 3], [0, 1, 2, 3], [0, 4], [0, 1, 4], [0, 2, 4], [0, 1, 2, 4], [0, 3, 4], [0, 1, 3, 4], [0, 2, 3, 4], [0, 1, 2, 3, 4]], [0, 1, 2, 3, 4], 是, union_of_connected_subsets_sharing_basepoint_is_connected)
Wave6第十一層核對=(0, [[0], [0, 1], [0, 2], [0, 1, 2], [0, 3], [0, 1, 3], [0, 2, 3], [0, 1, 2, 3], [0, 4], [0, 1, 4], [0, 2, 4], [0, 1, 2, 4], [0, 3, 4], [0, 1, 3, 4], [0, 2, 3, 4], [0, 1, 2, 3, 4]], [0, 1, 2, 3, 4], 是, union_of_connected_subsets_sharing_basepoint_is_connected)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-connected-subsets · candidate
16. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-connected-subsets；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,5],[1,2,3,4]],"basepoint":0}。請依 [basepoint, all_containing_connected_subsets, their_union, union_connected, certificate] 欄序回答。
查看答案與解釋
(0, [[0], [0, 5]], [0, 5], 是, union_of_connected_subsets_sharing_basepoint_is_connected)
Wave6第十一層核對=(0, [[0], [0, 5]], [0, 5], 是, union_of_connected_subsets_sharing_basepoint_is_connected)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-connected-subsets · candidate
17. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-connected-subsets；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,1,5],[2,3,4]],"basepoint":0}。請依 [basepoint, all_containing_connected_subsets, their_union, union_connected, certificate] 欄序回答。
查看答案與解釋
(0, [[0], [0, 1], [0, 5], [0, 1, 5]], [0, 1, 5], 是, union_of_connected_subsets_sharing_basepoint_is_connected)
Wave6第十一層核對=(0, [[0], [0, 1], [0, 5], [0, 1, 5]], [0, 1, 5], 是, union_of_connected_subsets_sharing_basepoint_is_connected)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-connected-subsets · candidate
18. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-connected-subsets；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,2,5],[1,3,4]],"basepoint":0}。請依 [basepoint, all_containing_connected_subsets, their_union, union_connected, certificate] 欄序回答。
查看答案與解釋
(0, [[0], [0, 2], [0, 5], [0, 2, 5]], [0, 2, 5], 是, union_of_connected_subsets_sharing_basepoint_is_connected)
Wave6第十一層核對=(0, [[0], [0, 2], [0, 5], [0, 2, 5]], [0, 2, 5], 是, union_of_connected_subsets_sharing_basepoint_is_connected)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-connected-subsets · candidate
19. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-connected-subsets；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,1,2,5],[3,4]],"basepoint":0}。請依 [basepoint, all_containing_connected_subsets, their_union, union_connected, certificate] 欄序回答。
查看答案與解釋
(0, [[0], [0, 1], [0, 2], [0, 1, 2], [0, 5], [0, 1, 5], [0, 2, 5], [0, 1, 2, 5]], [0, 1, 2, 5], 是, union_of_connected_subsets_sharing_basepoint_is_connected)
Wave6第十一層核對=(0, [[0], [0, 1], [0, 2], [0, 1, 2], [0, 5], [0, 1, 5], [0, 2, 5], [0, 1, 2, 5]], [0, 1, 2, 5], 是, union_of_connected_subsets_sharing_basepoint_is_connected)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-connected-subsets · candidate
20. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-connected-subsets；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,3,5],[1,2,4]],"basepoint":0}。請依 [basepoint, all_containing_connected_subsets, their_union, union_connected, certificate] 欄序回答。
查看答案與解釋
(0, [[0], [0, 3], [0, 5], [0, 3, 5]], [0, 3, 5], 是, union_of_connected_subsets_sharing_basepoint_is_connected)
Wave6第十一層核對=(0, [[0], [0, 3], [0, 5], [0, 3, 5]], [0, 3, 5], 是, union_of_connected_subsets_sharing_basepoint_is_connected)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-connected-subsets · candidate
21. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-connected-subsets；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,1,3,5],[2,4]],"basepoint":0}。請依 [basepoint, all_containing_connected_subsets, their_union, union_connected, certificate] 欄序回答。
查看答案與解釋
(0, [[0], [0, 1], [0, 3], [0, 1, 3], [0, 5], [0, 1, 5], [0, 3, 5], [0, 1, 3, 5]], [0, 1, 3, 5], 是, union_of_connected_subsets_sharing_basepoint_is_connected)
Wave6第十一層核對=(0, [[0], [0, 1], [0, 3], [0, 1, 3], [0, 5], [0, 1, 5], [0, 3, 5], [0, 1, 3, 5]], [0, 1, 3, 5], 是, union_of_connected_subsets_sharing_basepoint_is_connected)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-connected-subsets · candidate
22. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-connected-subsets；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,2,3,5],[1,4]],"basepoint":0}。請依 [basepoint, all_containing_connected_subsets, their_union, union_connected, certificate] 欄序回答。
查看答案與解釋
(0, [[0], [0, 2], [0, 3], [0, 2, 3], [0, 5], [0, 2, 5], [0, 3, 5], [0, 2, 3, 5]], [0, 2, 3, 5], 是, union_of_connected_subsets_sharing_basepoint_is_connected)
Wave6第十一層核對=(0, [[0], [0, 2], [0, 3], [0, 2, 3], [0, 5], [0, 2, 5], [0, 3, 5], [0, 2, 3, 5]], [0, 2, 3, 5], 是, union_of_connected_subsets_sharing_basepoint_is_connected)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-connected-subsets · candidate
23. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-connected-subsets；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,1,2,3,5],[4]],"basepoint":0}。請依 [basepoint, all_containing_connected_subsets, their_union, union_connected, certificate] 欄序回答。
查看答案與解釋
(0, [[0], [0, 1], [0, 2], [0, 1, 2], [0, 3], [0, 1, 3], [0, 2, 3], [0, 1, 2, 3], [0, 5], [0, 1, 5], [0, 2, 5], [0, 1, 2, 5], [0, 3, 5], [0, 1, 3, 5], [0, 2, 3, 5], [0, 1, 2, 3, 5]], [0, 1, 2, 3, 5], 是, union_of_connected_subsets_sharing_basepoint_is_connected)
Wave6第十一層核對=(0, [[0], [0, 1], [0, 2], [0, 1, 2], [0, 3], [0, 1, 3], [0, 2, 3], [0, 1, 2, 3], [0, 5], [0, 1, 5], [0, 2, 5], [0, 1, 2, 5], [0, 3, 5], [0, 1, 3, 5], [0, 2, 3, 5], [0, 1, 2, 3, 5]], [0, 1, 2, 3, 5], 是, union_of_connected_subsets_sharing_basepoint_is_connected)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-connected-subsets · candidate
24. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-connected-subsets；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,4,5],[1,2,3]],"basepoint":0}。請依 [basepoint, all_containing_connected_subsets, their_union, union_connected, certificate] 欄序回答。
查看答案與解釋
(0, [[0], [0, 4], [0, 5], [0, 4, 5]], [0, 4, 5], 是, union_of_connected_subsets_sharing_basepoint_is_connected)
Wave6第十一層核對=(0, [[0], [0, 4], [0, 5], [0, 4, 5]], [0, 4, 5], 是, union_of_connected_subsets_sharing_basepoint_is_connected)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-connected-subsets · candidate
25. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-connected-subsets；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,1,4,5],[2,3]],"basepoint":0}。請依 [basepoint, all_containing_connected_subsets, their_union, union_connected, certificate] 欄序回答。
查看答案與解釋
(0, [[0], [0, 1], [0, 4], [0, 1, 4], [0, 5], [0, 1, 5], [0, 4, 5], [0, 1, 4, 5]], [0, 1, 4, 5], 是, union_of_connected_subsets_sharing_basepoint_is_connected)
Wave6第十一層核對=(0, [[0], [0, 1], [0, 4], [0, 1, 4], [0, 5], [0, 1, 5], [0, 4, 5], [0, 1, 4, 5]], [0, 1, 4, 5], 是, union_of_connected_subsets_sharing_basepoint_is_connected)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-connected-subsets · candidate
26. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-maximality；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,1],[2,3,4,5]],"basepoint":0}。請依 [basepoint, component, all_containing_connected_subsets, inclusion_maximal, closed, certificate] 欄序回答。
查看答案與解釋
(0, [0, 1], [[0], [0, 1]], 是, 是, unique_inclusion_maximal_connected_subset)
Wave6第十一層核對=(0, [0, 1], [[0], [0, 1]], 是, 是, unique_inclusion_maximal_connected_subset)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-maximality · candidate
27. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-maximality；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,2],[1,3,4,5]],"basepoint":0}。請依 [basepoint, component, all_containing_connected_subsets, inclusion_maximal, closed, certificate] 欄序回答。
查看答案與解釋
(0, [0, 2], [[0], [0, 2]], 是, 是, unique_inclusion_maximal_connected_subset)
Wave6第十一層核對=(0, [0, 2], [[0], [0, 2]], 是, 是, unique_inclusion_maximal_connected_subset)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-maximality · candidate
28. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-maximality；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,1,2],[3,4,5]],"basepoint":0}。請依 [basepoint, component, all_containing_connected_subsets, inclusion_maximal, closed, certificate] 欄序回答。
查看答案與解釋
(0, [0, 1, 2], [[0], [0, 1], [0, 2], [0, 1, 2]], 是, 是, unique_inclusion_maximal_connected_subset)
Wave6第十一層核對=(0, [0, 1, 2], [[0], [0, 1], [0, 2], [0, 1, 2]], 是, 是, unique_inclusion_maximal_connected_subset)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-maximality · candidate
29. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-maximality；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,3],[1,2,4,5]],"basepoint":0}。請依 [basepoint, component, all_containing_connected_subsets, inclusion_maximal, closed, certificate] 欄序回答。
查看答案與解釋
(0, [0, 3], [[0], [0, 3]], 是, 是, unique_inclusion_maximal_connected_subset)
Wave6第十一層核對=(0, [0, 3], [[0], [0, 3]], 是, 是, unique_inclusion_maximal_connected_subset)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-maximality · candidate
30. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-maximality；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,1,3],[2,4,5]],"basepoint":0}。請依 [basepoint, component, all_containing_connected_subsets, inclusion_maximal, closed, certificate] 欄序回答。
查看答案與解釋
(0, [0, 1, 3], [[0], [0, 1], [0, 3], [0, 1, 3]], 是, 是, unique_inclusion_maximal_connected_subset)
Wave6第十一層核對=(0, [0, 1, 3], [[0], [0, 1], [0, 3], [0, 1, 3]], 是, 是, unique_inclusion_maximal_connected_subset)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-maximality · candidate
31. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-maximality；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,2,3],[1,4,5]],"basepoint":0}。請依 [basepoint, component, all_containing_connected_subsets, inclusion_maximal, closed, certificate] 欄序回答。
查看答案與解釋
(0, [0, 2, 3], [[0], [0, 2], [0, 3], [0, 2, 3]], 是, 是, unique_inclusion_maximal_connected_subset)
Wave6第十一層核對=(0, [0, 2, 3], [[0], [0, 2], [0, 3], [0, 2, 3]], 是, 是, unique_inclusion_maximal_connected_subset)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-maximality · candidate
32. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-maximality；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,1,2,3],[4,5]],"basepoint":0}。請依 [basepoint, component, all_containing_connected_subsets, inclusion_maximal, closed, certificate] 欄序回答。
查看答案與解釋
(0, [0, 1, 2, 3], [[0], [0, 1], [0, 2], [0, 1, 2], [0, 3], [0, 1, 3], [0, 2, 3], [0, 1, 2, 3]], 是, 是, unique_inclusion_maximal_connected_subset)
Wave6第十一層核對=(0, [0, 1, 2, 3], [[0], [0, 1], [0, 2], [0, 1, 2], [0, 3], [0, 1, 3], [0, 2, 3], [0, 1, 2, 3]], 是, 是, unique_inclusion_maximal_connected_subset)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-maximality · candidate
33. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-maximality；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,4],[1,2,3,5]],"basepoint":0}。請依 [basepoint, component, all_containing_connected_subsets, inclusion_maximal, closed, certificate] 欄序回答。
查看答案與解釋
(0, [0, 4], [[0], [0, 4]], 是, 是, unique_inclusion_maximal_connected_subset)
Wave6第十一層核對=(0, [0, 4], [[0], [0, 4]], 是, 是, unique_inclusion_maximal_connected_subset)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-maximality · candidate
34. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-maximality；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,1,4],[2,3,5]],"basepoint":0}。請依 [basepoint, component, all_containing_connected_subsets, inclusion_maximal, closed, certificate] 欄序回答。
查看答案與解釋
(0, [0, 1, 4], [[0], [0, 1], [0, 4], [0, 1, 4]], 是, 是, unique_inclusion_maximal_connected_subset)
Wave6第十一層核對=(0, [0, 1, 4], [[0], [0, 1], [0, 4], [0, 1, 4]], 是, 是, unique_inclusion_maximal_connected_subset)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-maximality · candidate
35. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-maximality；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,2,4],[1,3,5]],"basepoint":0}。請依 [basepoint, component, all_containing_connected_subsets, inclusion_maximal, closed, certificate] 欄序回答。
查看答案與解釋
(0, [0, 2, 4], [[0], [0, 2], [0, 4], [0, 2, 4]], 是, 是, unique_inclusion_maximal_connected_subset)
Wave6第十一層核對=(0, [0, 2, 4], [[0], [0, 2], [0, 4], [0, 2, 4]], 是, 是, unique_inclusion_maximal_connected_subset)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-maximality · candidate
36. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-maximality；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,1,2,4],[3,5]],"basepoint":0}。請依 [basepoint, component, all_containing_connected_subsets, inclusion_maximal, closed, certificate] 欄序回答。
查看答案與解釋
(0, [0, 1, 2, 4], [[0], [0, 1], [0, 2], [0, 1, 2], [0, 4], [0, 1, 4], [0, 2, 4], [0, 1, 2, 4]], 是, 是, unique_inclusion_maximal_connected_subset)
Wave6第十一層核對=(0, [0, 1, 2, 4], [[0], [0, 1], [0, 2], [0, 1, 2], [0, 4], [0, 1, 4], [0, 2, 4], [0, 1, 2, 4]], 是, 是, unique_inclusion_maximal_connected_subset)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-maximality · candidate
37. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-maximality；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,3,4],[1,2,5]],"basepoint":0}。請依 [basepoint, component, all_containing_connected_subsets, inclusion_maximal, closed, certificate] 欄序回答。
查看答案與解釋
(0, [0, 3, 4], [[0], [0, 3], [0, 4], [0, 3, 4]], 是, 是, unique_inclusion_maximal_connected_subset)
Wave6第十一層核對=(0, [0, 3, 4], [[0], [0, 3], [0, 4], [0, 3, 4]], 是, 是, unique_inclusion_maximal_connected_subset)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-maximality · candidate
38. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-maximality；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,1,3,4],[2,5]],"basepoint":0}。請依 [basepoint, component, all_containing_connected_subsets, inclusion_maximal, closed, certificate] 欄序回答。
查看答案與解釋
(0, [0, 1, 3, 4], [[0], [0, 1], [0, 3], [0, 1, 3], [0, 4], [0, 1, 4], [0, 3, 4], [0, 1, 3, 4]], 是, 是, unique_inclusion_maximal_connected_subset)
Wave6第十一層核對=(0, [0, 1, 3, 4], [[0], [0, 1], [0, 3], [0, 1, 3], [0, 4], [0, 1, 4], [0, 3, 4], [0, 1, 3, 4]], 是, 是, unique_inclusion_maximal_connected_subset)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-maximality · candidate
39. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-maximality；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,2,3,4],[1,5]],"basepoint":0}。請依 [basepoint, component, all_containing_connected_subsets, inclusion_maximal, closed, certificate] 欄序回答。
查看答案與解釋
(0, [0, 2, 3, 4], [[0], [0, 2], [0, 3], [0, 2, 3], [0, 4], [0, 2, 4], [0, 3, 4], [0, 2, 3, 4]], 是, 是, unique_inclusion_maximal_connected_subset)
Wave6第十一層核對=(0, [0, 2, 3, 4], [[0], [0, 2], [0, 3], [0, 2, 3], [0, 4], [0, 2, 4], [0, 3, 4], [0, 2, 3, 4]], 是, 是, unique_inclusion_maximal_connected_subset)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-maximality · candidate
40. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-maximality；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,1,2,3,4],[5]],"basepoint":0}。請依 [basepoint, component, all_containing_connected_subsets, inclusion_maximal, closed, certificate] 欄序回答。
查看答案與解釋
(0, [0, 1, 2, 3, 4], [[0], [0, 1], [0, 2], [0, 1, 2], [0, 3], [0, 1, 3], [0, 2, 3], [0, 1, 2, 3], [0, 4], [0, 1, 4], [0, 2, 4], [0, 1, 2, 4], [0, 3, 4], [0, 1, 3, 4], [0, 2, 3, 4], [0, 1, 2, 3, 4]], 是, 是, unique_inclusion_maximal_connected_subset)
Wave6第十一層核對=(0, [0, 1, 2, 3, 4], [[0], [0, 1], [0, 2], [0, 1, 2], [0, 3], [0, 1, 3], [0, 2, 3], [0, 1, 2, 3], [0, 4], [0, 1, 4], [0, 2, 4], [0, 1, 2, 4], [0, 3, 4], [0, 1, 3, 4], [0, 2, 3, 4], [0, 1, 2, 3, 4]], 是, 是, unique_inclusion_maximal_connected_subset)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-maximality · candidate
41. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-maximality；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,5],[1,2,3,4]],"basepoint":0}。請依 [basepoint, component, all_containing_connected_subsets, inclusion_maximal, closed, certificate] 欄序回答。
查看答案與解釋
(0, [0, 5], [[0], [0, 5]], 是, 是, unique_inclusion_maximal_connected_subset)
Wave6第十一層核對=(0, [0, 5], [[0], [0, 5]], 是, 是, unique_inclusion_maximal_connected_subset)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-maximality · candidate
42. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-maximality；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,1,5],[2,3,4]],"basepoint":0}。請依 [basepoint, component, all_containing_connected_subsets, inclusion_maximal, closed, certificate] 欄序回答。
查看答案與解釋
(0, [0, 1, 5], [[0], [0, 1], [0, 5], [0, 1, 5]], 是, 是, unique_inclusion_maximal_connected_subset)
Wave6第十一層核對=(0, [0, 1, 5], [[0], [0, 1], [0, 5], [0, 1, 5]], 是, 是, unique_inclusion_maximal_connected_subset)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-maximality · candidate
43. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-maximality；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,2,5],[1,3,4]],"basepoint":0}。請依 [basepoint, component, all_containing_connected_subsets, inclusion_maximal, closed, certificate] 欄序回答。
查看答案與解釋
(0, [0, 2, 5], [[0], [0, 2], [0, 5], [0, 2, 5]], 是, 是, unique_inclusion_maximal_connected_subset)
Wave6第十一層核對=(0, [0, 2, 5], [[0], [0, 2], [0, 5], [0, 2, 5]], 是, 是, unique_inclusion_maximal_connected_subset)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-maximality · candidate
44. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-maximality；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,1,2,5],[3,4]],"basepoint":0}。請依 [basepoint, component, all_containing_connected_subsets, inclusion_maximal, closed, certificate] 欄序回答。
查看答案與解釋
(0, [0, 1, 2, 5], [[0], [0, 1], [0, 2], [0, 1, 2], [0, 5], [0, 1, 5], [0, 2, 5], [0, 1, 2, 5]], 是, 是, unique_inclusion_maximal_connected_subset)
Wave6第十一層核對=(0, [0, 1, 2, 5], [[0], [0, 1], [0, 2], [0, 1, 2], [0, 5], [0, 1, 5], [0, 2, 5], [0, 1, 2, 5]], 是, 是, unique_inclusion_maximal_connected_subset)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-maximality · candidate
45. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-maximality；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,3,5],[1,2,4]],"basepoint":0}。請依 [basepoint, component, all_containing_connected_subsets, inclusion_maximal, closed, certificate] 欄序回答。
查看答案與解釋
(0, [0, 3, 5], [[0], [0, 3], [0, 5], [0, 3, 5]], 是, 是, unique_inclusion_maximal_connected_subset)
Wave6第十一層核對=(0, [0, 3, 5], [[0], [0, 3], [0, 5], [0, 3, 5]], 是, 是, unique_inclusion_maximal_connected_subset)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-maximality · candidate
46. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-maximality；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,1,3,5],[2,4]],"basepoint":0}。請依 [basepoint, component, all_containing_connected_subsets, inclusion_maximal, closed, certificate] 欄序回答。
查看答案與解釋
(0, [0, 1, 3, 5], [[0], [0, 1], [0, 3], [0, 1, 3], [0, 5], [0, 1, 5], [0, 3, 5], [0, 1, 3, 5]], 是, 是, unique_inclusion_maximal_connected_subset)
Wave6第十一層核對=(0, [0, 1, 3, 5], [[0], [0, 1], [0, 3], [0, 1, 3], [0, 5], [0, 1, 5], [0, 3, 5], [0, 1, 3, 5]], 是, 是, unique_inclusion_maximal_connected_subset)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-maximality · candidate
47. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-maximality；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,2,3,5],[1,4]],"basepoint":0}。請依 [basepoint, component, all_containing_connected_subsets, inclusion_maximal, closed, certificate] 欄序回答。
查看答案與解釋
(0, [0, 2, 3, 5], [[0], [0, 2], [0, 3], [0, 2, 3], [0, 5], [0, 2, 5], [0, 3, 5], [0, 2, 3, 5]], 是, 是, unique_inclusion_maximal_connected_subset)
Wave6第十一層核對=(0, [0, 2, 3, 5], [[0], [0, 2], [0, 3], [0, 2, 3], [0, 5], [0, 2, 5], [0, 3, 5], [0, 2, 3, 5]], 是, 是, unique_inclusion_maximal_connected_subset)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-maximality · candidate
48. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-maximality；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,1,2,3,5],[4]],"basepoint":0}。請依 [basepoint, component, all_containing_connected_subsets, inclusion_maximal, closed, certificate] 欄序回答。
查看答案與解釋
(0, [0, 1, 2, 3, 5], [[0], [0, 1], [0, 2], [0, 1, 2], [0, 3], [0, 1, 3], [0, 2, 3], [0, 1, 2, 3], [0, 5], [0, 1, 5], [0, 2, 5], [0, 1, 2, 5], [0, 3, 5], [0, 1, 3, 5], [0, 2, 3, 5], [0, 1, 2, 3, 5]], 是, 是, unique_inclusion_maximal_connected_subset)
Wave6第十一層核對=(0, [0, 1, 2, 3, 5], [[0], [0, 1], [0, 2], [0, 1, 2], [0, 3], [0, 1, 3], [0, 2, 3], [0, 1, 2, 3], [0, 5], [0, 1, 5], [0, 2, 5], [0, 1, 2, 5], [0, 3, 5], [0, 1, 3, 5], [0, 2, 3, 5], [0, 1, 2, 3, 5]], 是, 是, unique_inclusion_maximal_connected_subset)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-maximality · candidate
49. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-maximality；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,4,5],[1,2,3]],"basepoint":0}。請依 [basepoint, component, all_containing_connected_subsets, inclusion_maximal, closed, certificate] 欄序回答。
查看答案與解釋
(0, [0, 4, 5], [[0], [0, 4], [0, 5], [0, 4, 5]], 是, 是, unique_inclusion_maximal_connected_subset)
Wave6第十一層核對=(0, [0, 4, 5], [[0], [0, 4], [0, 5], [0, 4, 5]], 是, 是, unique_inclusion_maximal_connected_subset)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-maximality · candidate
50. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-maximality；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,1,4,5],[2,3]],"basepoint":0}。請依 [basepoint, component, all_containing_connected_subsets, inclusion_maximal, closed, certificate] 欄序回答。
查看答案與解釋
(0, [0, 1, 4, 5], [[0], [0, 1], [0, 4], [0, 1, 4], [0, 5], [0, 1, 5], [0, 4, 5], [0, 1, 4, 5]], 是, 是, unique_inclusion_maximal_connected_subset)
Wave6第十一層核對=(0, [0, 1, 4, 5], [[0], [0, 1], [0, 4], [0, 1, 4], [0, 5], [0, 1, 5], [0, 4, 5], [0, 1, 4, 5]], 是, 是, unique_inclusion_maximal_connected_subset)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-maximality · candidate
51. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-partition；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,1],[2,3,4,5]]}。請依 [components, pairwise_disjoint, cover, closed_flags, open_flags, finite_partition_certificate, certificate] 欄序回答。
查看答案與解釋
([[0, 1], [2, 3, 4, 5]], 是, 是, [是, 是], [是, 是], 是, finite_components_partition_and_are_clopen_finite_specific)
Wave6第十一層核對=([[0, 1], [2, 3, 4, 5]], 是, 是, [是, 是], [是, 是], 是, finite_components_partition_and_are_clopen_finite_specific)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-partition · candidate
52. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-partition；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,2],[1,3,4,5]]}。請依 [components, pairwise_disjoint, cover, closed_flags, open_flags, finite_partition_certificate, certificate] 欄序回答。
查看答案與解釋
([[0, 2], [1, 3, 4, 5]], 是, 是, [是, 是], [是, 是], 是, finite_components_partition_and_are_clopen_finite_specific)
Wave6第十一層核對=([[0, 2], [1, 3, 4, 5]], 是, 是, [是, 是], [是, 是], 是, finite_components_partition_and_are_clopen_finite_specific)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-partition · candidate
53. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-partition；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,1,2],[3,4,5]]}。請依 [components, pairwise_disjoint, cover, closed_flags, open_flags, finite_partition_certificate, certificate] 欄序回答。
查看答案與解釋
([[0, 1, 2], [3, 4, 5]], 是, 是, [是, 是], [是, 是], 是, finite_components_partition_and_are_clopen_finite_specific)
Wave6第十一層核對=([[0, 1, 2], [3, 4, 5]], 是, 是, [是, 是], [是, 是], 是, finite_components_partition_and_are_clopen_finite_specific)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-partition · candidate
54. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-partition；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,3],[1,2,4,5]]}。請依 [components, pairwise_disjoint, cover, closed_flags, open_flags, finite_partition_certificate, certificate] 欄序回答。
查看答案與解釋
([[0, 3], [1, 2, 4, 5]], 是, 是, [是, 是], [是, 是], 是, finite_components_partition_and_are_clopen_finite_specific)
Wave6第十一層核對=([[0, 3], [1, 2, 4, 5]], 是, 是, [是, 是], [是, 是], 是, finite_components_partition_and_are_clopen_finite_specific)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-partition · candidate
55. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-partition；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,1,3],[2,4,5]]}。請依 [components, pairwise_disjoint, cover, closed_flags, open_flags, finite_partition_certificate, certificate] 欄序回答。
查看答案與解釋
([[0, 1, 3], [2, 4, 5]], 是, 是, [是, 是], [是, 是], 是, finite_components_partition_and_are_clopen_finite_specific)
Wave6第十一層核對=([[0, 1, 3], [2, 4, 5]], 是, 是, [是, 是], [是, 是], 是, finite_components_partition_and_are_clopen_finite_specific)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-partition · candidate
56. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-partition；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,2,3],[1,4,5]]}。請依 [components, pairwise_disjoint, cover, closed_flags, open_flags, finite_partition_certificate, certificate] 欄序回答。
查看答案與解釋
([[0, 2, 3], [1, 4, 5]], 是, 是, [是, 是], [是, 是], 是, finite_components_partition_and_are_clopen_finite_specific)
Wave6第十一層核對=([[0, 2, 3], [1, 4, 5]], 是, 是, [是, 是], [是, 是], 是, finite_components_partition_and_are_clopen_finite_specific)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-partition · candidate
57. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-partition；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,1,2,3],[4,5]]}。請依 [components, pairwise_disjoint, cover, closed_flags, open_flags, finite_partition_certificate, certificate] 欄序回答。
查看答案與解釋
([[0, 1, 2, 3], [4, 5]], 是, 是, [是, 是], [是, 是], 是, finite_components_partition_and_are_clopen_finite_specific)
Wave6第十一層核對=([[0, 1, 2, 3], [4, 5]], 是, 是, [是, 是], [是, 是], 是, finite_components_partition_and_are_clopen_finite_specific)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-partition · candidate
58. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-partition；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,4],[1,2,3,5]]}。請依 [components, pairwise_disjoint, cover, closed_flags, open_flags, finite_partition_certificate, certificate] 欄序回答。
查看答案與解釋
([[0, 4], [1, 2, 3, 5]], 是, 是, [是, 是], [是, 是], 是, finite_components_partition_and_are_clopen_finite_specific)
Wave6第十一層核對=([[0, 4], [1, 2, 3, 5]], 是, 是, [是, 是], [是, 是], 是, finite_components_partition_and_are_clopen_finite_specific)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-partition · candidate
59. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-partition；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,1,4],[2,3,5]]}。請依 [components, pairwise_disjoint, cover, closed_flags, open_flags, finite_partition_certificate, certificate] 欄序回答。
查看答案與解釋
([[0, 1, 4], [2, 3, 5]], 是, 是, [是, 是], [是, 是], 是, finite_components_partition_and_are_clopen_finite_specific)
Wave6第十一層核對=([[0, 1, 4], [2, 3, 5]], 是, 是, [是, 是], [是, 是], 是, finite_components_partition_and_are_clopen_finite_specific)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-partition · candidate
60. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-partition；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,2,4],[1,3,5]]}。請依 [components, pairwise_disjoint, cover, closed_flags, open_flags, finite_partition_certificate, certificate] 欄序回答。
查看答案與解釋
([[0, 2, 4], [1, 3, 5]], 是, 是, [是, 是], [是, 是], 是, finite_components_partition_and_are_clopen_finite_specific)
Wave6第十一層核對=([[0, 2, 4], [1, 3, 5]], 是, 是, [是, 是], [是, 是], 是, finite_components_partition_and_are_clopen_finite_specific)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-partition · candidate
61. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-partition；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,1,2,4],[3,5]]}。請依 [components, pairwise_disjoint, cover, closed_flags, open_flags, finite_partition_certificate, certificate] 欄序回答。
查看答案與解釋
([[0, 1, 2, 4], [3, 5]], 是, 是, [是, 是], [是, 是], 是, finite_components_partition_and_are_clopen_finite_specific)
Wave6第十一層核對=([[0, 1, 2, 4], [3, 5]], 是, 是, [是, 是], [是, 是], 是, finite_components_partition_and_are_clopen_finite_specific)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-partition · candidate
62. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-partition；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,3,4],[1,2,5]]}。請依 [components, pairwise_disjoint, cover, closed_flags, open_flags, finite_partition_certificate, certificate] 欄序回答。
查看答案與解釋
([[0, 3, 4], [1, 2, 5]], 是, 是, [是, 是], [是, 是], 是, finite_components_partition_and_are_clopen_finite_specific)
Wave6第十一層核對=([[0, 3, 4], [1, 2, 5]], 是, 是, [是, 是], [是, 是], 是, finite_components_partition_and_are_clopen_finite_specific)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-partition · candidate
63. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-partition；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,1,3,4],[2,5]]}。請依 [components, pairwise_disjoint, cover, closed_flags, open_flags, finite_partition_certificate, certificate] 欄序回答。
查看答案與解釋
([[0, 1, 3, 4], [2, 5]], 是, 是, [是, 是], [是, 是], 是, finite_components_partition_and_are_clopen_finite_specific)
Wave6第十一層核對=([[0, 1, 3, 4], [2, 5]], 是, 是, [是, 是], [是, 是], 是, finite_components_partition_and_are_clopen_finite_specific)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-partition · candidate
64. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-partition；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,2,3,4],[1,5]]}。請依 [components, pairwise_disjoint, cover, closed_flags, open_flags, finite_partition_certificate, certificate] 欄序回答。
查看答案與解釋
([[0, 2, 3, 4], [1, 5]], 是, 是, [是, 是], [是, 是], 是, finite_components_partition_and_are_clopen_finite_specific)
Wave6第十一層核對=([[0, 2, 3, 4], [1, 5]], 是, 是, [是, 是], [是, 是], 是, finite_components_partition_and_are_clopen_finite_specific)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-partition · candidate
65. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-partition；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,1,2,3,4],[5]]}。請依 [components, pairwise_disjoint, cover, closed_flags, open_flags, finite_partition_certificate, certificate] 欄序回答。
查看答案與解釋
([[0, 1, 2, 3, 4], [5]], 是, 是, [是, 是], [是, 是], 是, finite_components_partition_and_are_clopen_finite_specific)
Wave6第十一層核對=([[0, 1, 2, 3, 4], [5]], 是, 是, [是, 是], [是, 是], 是, finite_components_partition_and_are_clopen_finite_specific)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-partition · candidate
66. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-partition；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,5],[1,2,3,4]]}。請依 [components, pairwise_disjoint, cover, closed_flags, open_flags, finite_partition_certificate, certificate] 欄序回答。
查看答案與解釋
([[0, 5], [1, 2, 3, 4]], 是, 是, [是, 是], [是, 是], 是, finite_components_partition_and_are_clopen_finite_specific)
Wave6第十一層核對=([[0, 5], [1, 2, 3, 4]], 是, 是, [是, 是], [是, 是], 是, finite_components_partition_and_are_clopen_finite_specific)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-partition · candidate
67. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-partition；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,1,5],[2,3,4]]}。請依 [components, pairwise_disjoint, cover, closed_flags, open_flags, finite_partition_certificate, certificate] 欄序回答。
查看答案與解釋
([[0, 1, 5], [2, 3, 4]], 是, 是, [是, 是], [是, 是], 是, finite_components_partition_and_are_clopen_finite_specific)
Wave6第十一層核對=([[0, 1, 5], [2, 3, 4]], 是, 是, [是, 是], [是, 是], 是, finite_components_partition_and_are_clopen_finite_specific)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-partition · candidate
68. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-partition；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,2,5],[1,3,4]]}。請依 [components, pairwise_disjoint, cover, closed_flags, open_flags, finite_partition_certificate, certificate] 欄序回答。
查看答案與解釋
([[0, 2, 5], [1, 3, 4]], 是, 是, [是, 是], [是, 是], 是, finite_components_partition_and_are_clopen_finite_specific)
Wave6第十一層核對=([[0, 2, 5], [1, 3, 4]], 是, 是, [是, 是], [是, 是], 是, finite_components_partition_and_are_clopen_finite_specific)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-partition · candidate
69. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-partition；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,1,2,5],[3,4]]}。請依 [components, pairwise_disjoint, cover, closed_flags, open_flags, finite_partition_certificate, certificate] 欄序回答。
查看答案與解釋
([[0, 1, 2, 5], [3, 4]], 是, 是, [是, 是], [是, 是], 是, finite_components_partition_and_are_clopen_finite_specific)
Wave6第十一層核對=([[0, 1, 2, 5], [3, 4]], 是, 是, [是, 是], [是, 是], 是, finite_components_partition_and_are_clopen_finite_specific)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-partition · candidate
70. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-partition；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,3,5],[1,2,4]]}。請依 [components, pairwise_disjoint, cover, closed_flags, open_flags, finite_partition_certificate, certificate] 欄序回答。
查看答案與解釋
([[0, 3, 5], [1, 2, 4]], 是, 是, [是, 是], [是, 是], 是, finite_components_partition_and_are_clopen_finite_specific)
Wave6第十一層核對=([[0, 3, 5], [1, 2, 4]], 是, 是, [是, 是], [是, 是], 是, finite_components_partition_and_are_clopen_finite_specific)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-partition · candidate
71. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-partition；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,1,3,5],[2,4]]}。請依 [components, pairwise_disjoint, cover, closed_flags, open_flags, finite_partition_certificate, certificate] 欄序回答。
查看答案與解釋
([[0, 1, 3, 5], [2, 4]], 是, 是, [是, 是], [是, 是], 是, finite_components_partition_and_are_clopen_finite_specific)
Wave6第十一層核對=([[0, 1, 3, 5], [2, 4]], 是, 是, [是, 是], [是, 是], 是, finite_components_partition_and_are_clopen_finite_specific)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-partition · candidate
72. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-partition；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,2,3,5],[1,4]]}。請依 [components, pairwise_disjoint, cover, closed_flags, open_flags, finite_partition_certificate, certificate] 欄序回答。
查看答案與解釋
([[0, 2, 3, 5], [1, 4]], 是, 是, [是, 是], [是, 是], 是, finite_components_partition_and_are_clopen_finite_specific)
Wave6第十一層核對=([[0, 2, 3, 5], [1, 4]], 是, 是, [是, 是], [是, 是], 是, finite_components_partition_and_are_clopen_finite_specific)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-partition · candidate
73. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-partition；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,1,2,3,5],[4]]}。請依 [components, pairwise_disjoint, cover, closed_flags, open_flags, finite_partition_certificate, certificate] 欄序回答。
查看答案與解釋
([[0, 1, 2, 3, 5], [4]], 是, 是, [是, 是], [是, 是], 是, finite_components_partition_and_are_clopen_finite_specific)
Wave6第十一層核對=([[0, 1, 2, 3, 5], [4]], 是, 是, [是, 是], [是, 是], 是, finite_components_partition_and_are_clopen_finite_specific)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-partition · candidate
74. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-partition；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,4,5],[1,2,3]]}。請依 [components, pairwise_disjoint, cover, closed_flags, open_flags, finite_partition_certificate, certificate] 欄序回答。
查看答案與解釋
([[0, 4, 5], [1, 2, 3]], 是, 是, [是, 是], [是, 是], 是, finite_components_partition_and_are_clopen_finite_specific)
Wave6第十一層核對=([[0, 4, 5], [1, 2, 3]], 是, 是, [是, 是], [是, 是], 是, finite_components_partition_and_are_clopen_finite_specific)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-partition · candidate
75. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-partition；資料={"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,1,4,5],[2,3]]}。請依 [components, pairwise_disjoint, cover, closed_flags, open_flags, finite_partition_certificate, certificate] 欄序回答。
查看答案與解釋
([[0, 1, 4, 5], [2, 3]], 是, 是, [是, 是], [是, 是], 是, finite_components_partition_and_are_clopen_finite_specific)
Wave6第十一層核對=([[0, 1, 4, 5], [2, 3]], 是, 是, [是, 是], [是, 是], 是, finite_components_partition_and_are_clopen_finite_specific)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-partition · candidate
76. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-boundary；資料={"mode":"finite_clopen","model":{"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,1],[2,3,4,5]]}}。請依 [mode, components, closed_flags, open_flags, all_clopen, certificate] 欄序回答。
四種mode為6/5/6/8欄；finite components均clopen，不可造非open finite反例。graph與topology是不同結構；component極大是包含關係，不是全域最大基數。
查看答案與解釋
(finite_clopen, [[0, 1], [2, 3, 4, 5]], [是, 是], [是, 是], 是, finite_number_of_closed_components_makes_each_open)
Wave6第十一層核對=(finite_clopen, [[0, 1], [2, 3, 4, 5]], [是, 是], [是, 是], 是, finite_number_of_closed_components_makes_each_open)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-boundary · candidate
77. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-boundary；資料={"mode":"finite_no_nonopen_witness","model":{"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,2],[1,3,4,5]]}}。請依 [mode, components, all_clopen, general_nonopen_witness_claim, boundary] 欄序回答。
四種mode為6/5/6/8欄；finite components均clopen，不可造非open finite反例。graph與topology是不同結構；component極大是包含關係，不是全域最大基數。
查看答案與解釋
(finite_no_nonopen_witness, [[0, 2], [1, 3, 4, 5]], 是, 否, finite_models_cannot_witness_a_general_nonopen_component)
Wave6第十一層核對=(finite_no_nonopen_witness, [[0, 2], [1, 3, 4, 5]], 是, 否, finite_models_cannot_witness_a_general_nonopen_component)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-boundary · candidate
78. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-boundary；資料={"mode":"graph_confusion","model":{"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,1,2],[3,4,5]],"graph_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]]}}。請依 [mode, topological_components, graph_components, different_partitions, structure_identification_claim, boundary] 欄序回答。
四種mode為6/5/6/8欄；finite components均clopen，不可造非open finite反例。graph與topology是不同結構；component極大是包含關係，不是全域最大基數。
查看答案與解釋
(graph_confusion, [[0, 1, 2], [3, 4, 5]], [[0, 1, 2, 3, 4, 5]], 是, 否, same_carrier_different_structures_give_different_components)
Wave6第十一層核對=(graph_confusion, [[0, 1, 2], [3, 4, 5]], [[0, 1, 2, 3, 4, 5]], 是, 否, same_carrier_different_structures_give_different_components)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-boundary · candidate
79. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-boundary；資料={"mode":"cardinality_not_definition","model":{"points":[0,1,2],"topology":[[],[0,1,2],[0],[1,2]],"basepoint":0}}。請依 [mode, basepoint, own_component, larger_other_component, own_cardinality, other_cardinality, global_cardinality_definition_claim, boundary] 欄序回答。
四種mode為6/5/6/8欄；finite components均clopen，不可造非open finite反例。graph與topology是不同結構；component極大是包含關係，不是全域最大基數。
查看答案與解釋
(cardinality_not_definition, 0, [0], [1, 2], 1, 2, 否, component_is_inclusion_maximal_not_global_maximum_cardinality)
Wave6第十一層核對=(cardinality_not_definition, 0, [0], [1, 2], 1, 2, 否, component_is_inclusion_maximal_not_global_maximum_cardinality)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-boundary · candidate
80. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-boundary；資料={"mode":"finite_clopen","model":{"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,1,3],[2,4,5]]}}。請依 [mode, components, closed_flags, open_flags, all_clopen, certificate] 欄序回答。
四種mode為6/5/6/8欄；finite components均clopen，不可造非open finite反例。graph與topology是不同結構；component極大是包含關係，不是全域最大基數。
查看答案與解釋
(finite_clopen, [[0, 1, 3], [2, 4, 5]], [是, 是], [是, 是], 是, finite_number_of_closed_components_makes_each_open)
Wave6第十一層核對=(finite_clopen, [[0, 1, 3], [2, 4, 5]], [是, 是], [是, 是], 是, finite_number_of_closed_components_makes_each_open)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-boundary · candidate
81. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-boundary；資料={"mode":"finite_no_nonopen_witness","model":{"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,2,3],[1,4,5]]}}。請依 [mode, components, all_clopen, general_nonopen_witness_claim, boundary] 欄序回答。
四種mode為6/5/6/8欄；finite components均clopen，不可造非open finite反例。graph與topology是不同結構；component極大是包含關係，不是全域最大基數。
查看答案與解釋
(finite_no_nonopen_witness, [[0, 2, 3], [1, 4, 5]], 是, 否, finite_models_cannot_witness_a_general_nonopen_component)
Wave6第十一層核對=(finite_no_nonopen_witness, [[0, 2, 3], [1, 4, 5]], 是, 否, finite_models_cannot_witness_a_general_nonopen_component)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-boundary · candidate
82. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-boundary；資料={"mode":"graph_confusion","model":{"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,1,2,3],[4,5]],"graph_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]]}}。請依 [mode, topological_components, graph_components, different_partitions, structure_identification_claim, boundary] 欄序回答。
四種mode為6/5/6/8欄；finite components均clopen，不可造非open finite反例。graph與topology是不同結構；component極大是包含關係，不是全域最大基數。
查看答案與解釋
(graph_confusion, [[0, 1, 2, 3], [4, 5]], [[0, 1, 2, 3, 4, 5]], 是, 否, same_carrier_different_structures_give_different_components)
Wave6第十一層核對=(graph_confusion, [[0, 1, 2, 3], [4, 5]], [[0, 1, 2, 3, 4, 5]], 是, 否, same_carrier_different_structures_give_different_components)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-boundary · candidate
83. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-boundary；資料={"mode":"cardinality_not_definition","model":{"points":[0,1,2,3],"topology":[[],[0,1,2,3],[0],[1,2,3]],"basepoint":0}}。請依 [mode, basepoint, own_component, larger_other_component, own_cardinality, other_cardinality, global_cardinality_definition_claim, boundary] 欄序回答。
四種mode為6/5/6/8欄；finite components均clopen，不可造非open finite反例。graph與topology是不同結構；component極大是包含關係，不是全域最大基數。
查看答案與解釋
(cardinality_not_definition, 0, [0], [1, 2, 3], 1, 3, 否, component_is_inclusion_maximal_not_global_maximum_cardinality)
Wave6第十一層核對=(cardinality_not_definition, 0, [0], [1, 2, 3], 1, 3, 否, component_is_inclusion_maximal_not_global_maximum_cardinality)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-boundary · candidate
84. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-boundary；資料={"mode":"finite_clopen","model":{"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,1,4],[2,3,5]]}}。請依 [mode, components, closed_flags, open_flags, all_clopen, certificate] 欄序回答。
四種mode為6/5/6/8欄；finite components均clopen，不可造非open finite反例。graph與topology是不同結構；component極大是包含關係，不是全域最大基數。
查看答案與解釋
(finite_clopen, [[0, 1, 4], [2, 3, 5]], [是, 是], [是, 是], 是, finite_number_of_closed_components_makes_each_open)
Wave6第十一層核對=(finite_clopen, [[0, 1, 4], [2, 3, 5]], [是, 是], [是, 是], 是, finite_number_of_closed_components_makes_each_open)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-boundary · candidate
85. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-boundary；資料={"mode":"finite_no_nonopen_witness","model":{"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,2,4],[1,3,5]]}}。請依 [mode, components, all_clopen, general_nonopen_witness_claim, boundary] 欄序回答。
四種mode為6/5/6/8欄；finite components均clopen，不可造非open finite反例。graph與topology是不同結構；component極大是包含關係，不是全域最大基數。
查看答案與解釋
(finite_no_nonopen_witness, [[0, 2, 4], [1, 3, 5]], 是, 否, finite_models_cannot_witness_a_general_nonopen_component)
Wave6第十一層核對=(finite_no_nonopen_witness, [[0, 2, 4], [1, 3, 5]], 是, 否, finite_models_cannot_witness_a_general_nonopen_component)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-boundary · candidate
86. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-boundary；資料={"mode":"graph_confusion","model":{"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,1,2,4],[3,5]],"graph_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]]}}。請依 [mode, topological_components, graph_components, different_partitions, structure_identification_claim, boundary] 欄序回答。
四種mode為6/5/6/8欄；finite components均clopen，不可造非open finite反例。graph與topology是不同結構；component極大是包含關係，不是全域最大基數。
查看答案與解釋
(graph_confusion, [[0, 1, 2, 4], [3, 5]], [[0, 1, 2, 3, 4, 5]], 是, 否, same_carrier_different_structures_give_different_components)
Wave6第十一層核對=(graph_confusion, [[0, 1, 2, 4], [3, 5]], [[0, 1, 2, 3, 4, 5]], 是, 否, same_carrier_different_structures_give_different_components)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-boundary · candidate
87. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-boundary；資料={"mode":"cardinality_not_definition","model":{"points":[0,1,2,3,4],"topology":[[],[0,1,2,3,4],[0],[1,2,3,4]],"basepoint":0}}。請依 [mode, basepoint, own_component, larger_other_component, own_cardinality, other_cardinality, global_cardinality_definition_claim, boundary] 欄序回答。
四種mode為6/5/6/8欄；finite components均clopen，不可造非open finite反例。graph與topology是不同結構；component極大是包含關係，不是全域最大基數。
查看答案與解釋
(cardinality_not_definition, 0, [0], [1, 2, 3, 4], 1, 4, 否, component_is_inclusion_maximal_not_global_maximum_cardinality)
Wave6第十一層核對=(cardinality_not_definition, 0, [0], [1, 2, 3, 4], 1, 4, 否, component_is_inclusion_maximal_not_global_maximum_cardinality)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-boundary · candidate
88. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-boundary；資料={"mode":"finite_clopen","model":{"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,1,3,4],[2,5]]}}。請依 [mode, components, closed_flags, open_flags, all_clopen, certificate] 欄序回答。
四種mode為6/5/6/8欄；finite components均clopen，不可造非open finite反例。graph與topology是不同結構；component極大是包含關係，不是全域最大基數。
查看答案與解釋
(finite_clopen, [[0, 1, 3, 4], [2, 5]], [是, 是], [是, 是], 是, finite_number_of_closed_components_makes_each_open)
Wave6第十一層核對=(finite_clopen, [[0, 1, 3, 4], [2, 5]], [是, 是], [是, 是], 是, finite_number_of_closed_components_makes_each_open)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-boundary · candidate
89. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-boundary；資料={"mode":"finite_no_nonopen_witness","model":{"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,2,3,4],[1,5]]}}。請依 [mode, components, all_clopen, general_nonopen_witness_claim, boundary] 欄序回答。
四種mode為6/5/6/8欄；finite components均clopen，不可造非open finite反例。graph與topology是不同結構；component極大是包含關係，不是全域最大基數。
查看答案與解釋
(finite_no_nonopen_witness, [[0, 2, 3, 4], [1, 5]], 是, 否, finite_models_cannot_witness_a_general_nonopen_component)
Wave6第十一層核對=(finite_no_nonopen_witness, [[0, 2, 3, 4], [1, 5]], 是, 否, finite_models_cannot_witness_a_general_nonopen_component)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-boundary · candidate
90. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-boundary；資料={"mode":"graph_confusion","model":{"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,1,2,3,4],[5]],"graph_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]]}}。請依 [mode, topological_components, graph_components, different_partitions, structure_identification_claim, boundary] 欄序回答。
四種mode為6/5/6/8欄；finite components均clopen，不可造非open finite反例。graph與topology是不同結構；component極大是包含關係，不是全域最大基數。
查看答案與解釋
(graph_confusion, [[0, 1, 2, 3, 4], [5]], [[0, 1, 2, 3, 4, 5]], 是, 否, same_carrier_different_structures_give_different_components)
Wave6第十一層核對=(graph_confusion, [[0, 1, 2, 3, 4], [5]], [[0, 1, 2, 3, 4, 5]], 是, 否, same_carrier_different_structures_give_different_components)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-boundary · candidate
91. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-boundary；資料={"mode":"cardinality_not_definition","model":{"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0],[1,2,3,4,5]],"basepoint":0}}。請依 [mode, basepoint, own_component, larger_other_component, own_cardinality, other_cardinality, global_cardinality_definition_claim, boundary] 欄序回答。
四種mode為6/5/6/8欄；finite components均clopen，不可造非open finite反例。graph與topology是不同結構；component極大是包含關係，不是全域最大基數。
查看答案與解釋
(cardinality_not_definition, 0, [0], [1, 2, 3, 4, 5], 1, 5, 否, component_is_inclusion_maximal_not_global_maximum_cardinality)
Wave6第十一層核對=(cardinality_not_definition, 0, [0], [1, 2, 3, 4, 5], 1, 5, 否, component_is_inclusion_maximal_not_global_maximum_cardinality)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-boundary · candidate
92. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-boundary；資料={"mode":"finite_clopen","model":{"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,1,5],[2,3,4]]}}。請依 [mode, components, closed_flags, open_flags, all_clopen, certificate] 欄序回答。
四種mode為6/5/6/8欄；finite components均clopen，不可造非open finite反例。graph與topology是不同結構；component極大是包含關係，不是全域最大基數。
查看答案與解釋
(finite_clopen, [[0, 1, 5], [2, 3, 4]], [是, 是], [是, 是], 是, finite_number_of_closed_components_makes_each_open)
Wave6第十一層核對=(finite_clopen, [[0, 1, 5], [2, 3, 4]], [是, 是], [是, 是], 是, finite_number_of_closed_components_makes_each_open)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-boundary · candidate
93. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-boundary；資料={"mode":"finite_no_nonopen_witness","model":{"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,2,5],[1,3,4]]}}。請依 [mode, components, all_clopen, general_nonopen_witness_claim, boundary] 欄序回答。
四種mode為6/5/6/8欄；finite components均clopen，不可造非open finite反例。graph與topology是不同結構；component極大是包含關係，不是全域最大基數。
查看答案與解釋
(finite_no_nonopen_witness, [[0, 2, 5], [1, 3, 4]], 是, 否, finite_models_cannot_witness_a_general_nonopen_component)
Wave6第十一層核對=(finite_no_nonopen_witness, [[0, 2, 5], [1, 3, 4]], 是, 否, finite_models_cannot_witness_a_general_nonopen_component)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-boundary · candidate
94. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-boundary；資料={"mode":"graph_confusion","model":{"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,1,2,5],[3,4]],"graph_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]]}}。請依 [mode, topological_components, graph_components, different_partitions, structure_identification_claim, boundary] 欄序回答。
四種mode為6/5/6/8欄；finite components均clopen，不可造非open finite反例。graph與topology是不同結構；component極大是包含關係，不是全域最大基數。
查看答案與解釋
(graph_confusion, [[0, 1, 2, 5], [3, 4]], [[0, 1, 2, 3, 4, 5]], 是, 否, same_carrier_different_structures_give_different_components)
Wave6第十一層核對=(graph_confusion, [[0, 1, 2, 5], [3, 4]], [[0, 1, 2, 3, 4, 5]], 是, 否, same_carrier_different_structures_give_different_components)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-boundary · candidate
95. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-boundary；資料={"mode":"cardinality_not_definition","model":{"points":[0,1,2,3,4,5,6],"topology":[[],[0,1,2,3,4,5,6],[0],[1,2,3,4,5,6]],"basepoint":0}}。請依 [mode, basepoint, own_component, larger_other_component, own_cardinality, other_cardinality, global_cardinality_definition_claim, boundary] 欄序回答。
四種mode為6/5/6/8欄；finite components均clopen，不可造非open finite反例。graph與topology是不同結構；component極大是包含關係，不是全域最大基數。
查看答案與解釋
(cardinality_not_definition, 0, [0], [1, 2, 3, 4, 5, 6], 1, 6, 否, component_is_inclusion_maximal_not_global_maximum_cardinality)
Wave6第十一層核對=(cardinality_not_definition, 0, [0], [1, 2, 3, 4, 5, 6], 1, 6, 否, component_is_inclusion_maximal_not_global_maximum_cardinality)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-boundary · candidate
96. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-boundary；資料={"mode":"finite_clopen","model":{"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,1,3,5],[2,4]]}}。請依 [mode, components, closed_flags, open_flags, all_clopen, certificate] 欄序回答。
四種mode為6/5/6/8欄；finite components均clopen，不可造非open finite反例。graph與topology是不同結構；component極大是包含關係，不是全域最大基數。
查看答案與解釋
(finite_clopen, [[0, 1, 3, 5], [2, 4]], [是, 是], [是, 是], 是, finite_number_of_closed_components_makes_each_open)
Wave6第十一層核對=(finite_clopen, [[0, 1, 3, 5], [2, 4]], [是, 是], [是, 是], 是, finite_number_of_closed_components_makes_each_open)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-boundary · candidate
97. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-boundary；資料={"mode":"finite_no_nonopen_witness","model":{"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,2,3,5],[1,4]]}}。請依 [mode, components, all_clopen, general_nonopen_witness_claim, boundary] 欄序回答。
四種mode為6/5/6/8欄；finite components均clopen，不可造非open finite反例。graph與topology是不同結構；component極大是包含關係，不是全域最大基數。
查看答案與解釋
(finite_no_nonopen_witness, [[0, 2, 3, 5], [1, 4]], 是, 否, finite_models_cannot_witness_a_general_nonopen_component)
Wave6第十一層核對=(finite_no_nonopen_witness, [[0, 2, 3, 5], [1, 4]], 是, 否, finite_models_cannot_witness_a_general_nonopen_component)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-boundary · candidate
98. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-boundary；資料={"mode":"graph_confusion","model":{"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,1,2,3,5],[4]],"graph_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]]}}。請依 [mode, topological_components, graph_components, different_partitions, structure_identification_claim, boundary] 欄序回答。
四種mode為6/5/6/8欄；finite components均clopen，不可造非open finite反例。graph與topology是不同結構；component極大是包含關係，不是全域最大基數。
查看答案與解釋
(graph_confusion, [[0, 1, 2, 3, 5], [4]], [[0, 1, 2, 3, 4, 5]], 是, 否, same_carrier_different_structures_give_different_components)
Wave6第十一層核對=(graph_confusion, [[0, 1, 2, 3, 5], [4]], [[0, 1, 2, 3, 4, 5]], 是, 否, same_carrier_different_structures_give_different_components)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-boundary · candidate
99. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-boundary；資料={"mode":"cardinality_not_definition","model":{"points":[0,1,2,3,4,5,6,7],"topology":[[],[0,1,2,3,4,5,6,7],[0],[1,2,3,4,5,6,7]],"basepoint":0}}。請依 [mode, basepoint, own_component, larger_other_component, own_cardinality, other_cardinality, global_cardinality_definition_claim, boundary] 欄序回答。
四種mode為6/5/6/8欄；finite components均clopen，不可造非open finite反例。graph與topology是不同結構；component極大是包含關係，不是全域最大基數。
查看答案與解釋
(cardinality_not_definition, 0, [0], [1, 2, 3, 4, 5, 6, 7], 1, 7, 否, component_is_inclusion_maximal_not_global_maximum_cardinality)
Wave6第十一層核對=(cardinality_not_definition, 0, [0], [1, 2, 3, 4, 5, 6, 7], 1, 7, 否, component_is_inclusion_maximal_not_global_maximum_cardinality)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-boundary · candidate
100. 拓撲連通分支
subspace connectedness、包含關係maximality與完整component partition責任。操作=component-boundary；資料={"mode":"finite_clopen","model":{"points":[0,1,2,3,4,5],"topology":[[],[0,1,2,3,4,5],[0,1,4,5],[2,3]]}}。請依 [mode, components, closed_flags, open_flags, all_clopen, certificate] 欄序回答。
四種mode為6/5/6/8欄；finite components均clopen，不可造非open finite反例。graph與topology是不同結構；component極大是包含關係，不是全域最大基數。
查看答案與解釋
(finite_clopen, [[0, 1, 4, 5], [2, 3]], [是, 是], [是, 是], 是, finite_number_of_closed_components_makes_each_open)
Wave6第十一層核對=(finite_clopen, [[0, 1, 4, 5], [2, 3]], [是, 是], [是, 是], 是, finite_number_of_closed_components_makes_each_open)；依完整明示資料獨立重算；finite topology以全部subsets與opens枚舉並核closedness；finite-space clopen現象不得外推；graph components與最大基數connected subsets另有定義。
本題逐步詳解（AI 二次覆核）
拓撲連通分支 · qf-mod48-component-boundary · candidate
原始題目 JSONL · 驗收報告