# 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](https://ocme.evemisslab.com/data/i18n/question-output-protocols.json)



## 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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0001/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0002/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0003/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0004/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0005/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0006/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0007/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0008/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0009/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0010/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0011/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0012/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0013/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0014/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0015/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0016/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0017/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0018/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0019/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0020/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0021/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0022/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0023/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0024/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0025/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0026/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0027/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0028/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0029/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0030/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0031/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0032/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0033/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0034/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0035/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0036/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0037/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0038/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0039/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0040/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0041/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0042/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0043/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0044/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0045/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0046/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0047/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0048/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0049/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0050/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0051/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0052/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0053/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0054/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0055/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0056/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0057/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0058/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0059/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0060/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0061/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0062/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0063/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0064/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0065/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0066/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0067/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0068/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0069/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0070/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0071/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0072/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0073/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0074/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0075/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0076/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0077/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0078/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0079/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0080/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0081/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0082/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0083/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0084/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0085/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0086/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0087/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0088/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0089/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0090/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0091/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0092/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0093/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0094/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0095/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0096/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0097/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0098/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0099/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r07-topological-connected-component-0100/)

拓撲連通分支 · qf-mod48-component-boundary · candidate



[原始題目 JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261015-advance-20261117-r07-topological-connected-component-foundations/questions.jsonl) · [驗收報告](https://ocme.evemisslab.com/data/questions/batches/batch-20261015-advance-20261117-r07-topological-connected-component-foundations/validation-report.json)