# 子空間拓撲基礎 · 脈衝 R03

本批已通過 Schema、去重、來源快照與獨立答案重算；仍未標記為人工審定。

本題庫已有對應的中英逐步詳解。原題的 candidate 與英文 ai_candidate 狀態保留；AI 覆核、有限計算與 Lean 形式證明分開標示。

batch-20261014-advance-20261108-r03-subspace-topology-foundations · 2026-10-14 · 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. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-induced-topology；資料={"n":5,"parent_topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4]],"subset":[1,3,4]}。請依 [subset, induced_topology, open_count, topology_certificate, certificate] 欄序回答。

查看答案與解釋([1, 3, 4], [[], [1], [1, 3], [1, 3, 4]], 4, 是, all_parent_open_intersections_normalized)

Wave6第二層核對=([1, 3, 4], [[], [1], [1, 3], [1, 3, 4]], 4, 是, all_parent_open_intersections_normalized)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0001/)

子空間拓撲 · qf-mod39-subtop-induced-topology · candidate





## 2. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-induced-topology；資料={"n":5,"parent_topology":[[],[0],[0,1],[0,1,2],[0,1,2,3,4],[0,1,2,4]],"subset":[1,3,4]}。請依 [subset, induced_topology, open_count, topology_certificate, certificate] 欄序回答。

查看答案與解釋([1, 3, 4], [[], [1], [1, 3, 4], [1, 4]], 4, 是, all_parent_open_intersections_normalized)

Wave6第二層核對=([1, 3, 4], [[], [1], [1, 3, 4], [1, 4]], 4, 是, all_parent_open_intersections_normalized)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0002/)

子空間拓撲 · qf-mod39-subtop-induced-topology · candidate





## 3. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-induced-topology；資料={"n":5,"parent_topology":[[],[0],[0,1],[0,1,2,3],[0,1,2,3,4],[0,1,3]],"subset":[1,2,4]}。請依 [subset, induced_topology, open_count, topology_certificate, certificate] 欄序回答。

查看答案與解釋([1, 2, 4], [[], [1], [1, 2], [1, 2, 4]], 4, 是, all_parent_open_intersections_normalized)

Wave6第二層核對=([1, 2, 4], [[], [1], [1, 2], [1, 2, 4]], 4, 是, all_parent_open_intersections_normalized)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0003/)

子空間拓撲 · qf-mod39-subtop-induced-topology · candidate





## 4. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-induced-topology；資料={"n":5,"parent_topology":[[],[0],[0,1],[0,1,2,3,4],[0,1,3],[0,1,3,4]],"subset":[1,2,4]}。請依 [subset, induced_topology, open_count, topology_certificate, certificate] 欄序回答。

查看答案與解釋([1, 2, 4], [[], [1], [1, 2, 4], [1, 4]], 4, 是, all_parent_open_intersections_normalized)

Wave6第二層核對=([1, 2, 4], [[], [1], [1, 2, 4], [1, 4]], 4, 是, all_parent_open_intersections_normalized)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0004/)

子空間拓撲 · qf-mod39-subtop-induced-topology · candidate





## 5. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-induced-topology；資料={"n":5,"parent_topology":[[],[0],[0,1],[0,1,2,3,4],[0,1,2,4],[0,1,4]],"subset":[1,2,3]}。請依 [subset, induced_topology, open_count, topology_certificate, certificate] 欄序回答。

查看答案與解釋([1, 2, 3], [[], [1], [1, 2], [1, 2, 3]], 4, 是, all_parent_open_intersections_normalized)

Wave6第二層核對=([1, 2, 3], [[], [1], [1, 2], [1, 2, 3]], 4, 是, all_parent_open_intersections_normalized)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0005/)

子空間拓撲 · qf-mod39-subtop-induced-topology · candidate





## 6. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-induced-topology；資料={"n":5,"parent_topology":[[],[0],[0,1],[0,1,2,3,4],[0,1,3,4],[0,1,4]],"subset":[1,2,3]}。請依 [subset, induced_topology, open_count, topology_certificate, certificate] 欄序回答。

查看答案與解釋([1, 2, 3], [[], [1], [1, 2, 3], [1, 3]], 4, 是, all_parent_open_intersections_normalized)

Wave6第二層核對=([1, 2, 3], [[], [1], [1, 2, 3], [1, 3]], 4, 是, all_parent_open_intersections_normalized)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0006/)

子空間拓撲 · qf-mod39-subtop-induced-topology · candidate





## 7. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-induced-topology；資料={"n":5,"parent_topology":[[],[0],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,2]],"subset":[2,3,4]}。請依 [subset, induced_topology, open_count, topology_certificate, certificate] 欄序回答。

查看答案與解釋([2, 3, 4], [[], [2], [2, 3], [2, 3, 4]], 4, 是, all_parent_open_intersections_normalized)

Wave6第二層核對=([2, 3, 4], [[], [2], [2, 3], [2, 3, 4]], 4, 是, all_parent_open_intersections_normalized)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0007/)

子空間拓撲 · qf-mod39-subtop-induced-topology · candidate





## 8. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-induced-topology；資料={"n":5,"parent_topology":[[],[0],[0,1,2],[0,1,2,3,4],[0,1,2,4],[0,2]],"subset":[2,3,4]}。請依 [subset, induced_topology, open_count, topology_certificate, certificate] 欄序回答。

查看答案與解釋([2, 3, 4], [[], [2], [2, 3, 4], [2, 4]], 4, 是, all_parent_open_intersections_normalized)

Wave6第二層核對=([2, 3, 4], [[], [2], [2, 3, 4], [2, 4]], 4, 是, all_parent_open_intersections_normalized)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0008/)

子空間拓撲 · qf-mod39-subtop-induced-topology · candidate





## 9. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-induced-topology；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3],[0,1,2,3,4],[0,2],[0,2,3]],"subset":[1,2,4]}。請依 [subset, induced_topology, open_count, topology_certificate, certificate] 欄序回答。

查看答案與解釋([1, 2, 4], [[], [1, 2], [1, 2, 4], [2]], 4, 是, all_parent_open_intersections_normalized)

Wave6第二層核對=([1, 2, 4], [[], [1, 2], [1, 2, 4], [2]], 4, 是, all_parent_open_intersections_normalized)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0009/)

子空間拓撲 · qf-mod39-subtop-induced-topology · candidate





## 10. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-induced-topology；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2],[0,2,3],[0,2,3,4]],"subset":[1,2,4]}。請依 [subset, induced_topology, open_count, topology_certificate, certificate] 欄序回答。

查看答案與解釋([1, 2, 4], [[], [1, 2, 4], [2], [2, 4]], 4, 是, all_parent_open_intersections_normalized)

Wave6第二層核對=([1, 2, 4], [[], [1, 2, 4], [2], [2, 4]], 4, 是, all_parent_open_intersections_normalized)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0010/)

子空間拓撲 · qf-mod39-subtop-induced-topology · candidate





## 11. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-induced-topology；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,2,4],[0,2],[0,2,4]],"subset":[1,2,3]}。請依 [subset, induced_topology, open_count, topology_certificate, certificate] 欄序回答。

查看答案與解釋([1, 2, 3], [[], [1, 2], [1, 2, 3], [2]], 4, 是, all_parent_open_intersections_normalized)

Wave6第二層核對=([1, 2, 3], [[], [1, 2], [1, 2, 3], [2]], 4, 是, all_parent_open_intersections_normalized)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0011/)

子空間拓撲 · qf-mod39-subtop-induced-topology · candidate





## 12. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-induced-topology；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2],[0,2,3,4],[0,2,4]],"subset":[1,2,3]}。請依 [subset, induced_topology, open_count, topology_certificate, certificate] 欄序回答。

查看答案與解釋([1, 2, 3], [[], [1, 2, 3], [2], [2, 3]], 4, 是, all_parent_open_intersections_normalized)

Wave6第二層核對=([1, 2, 3], [[], [1, 2, 3], [2], [2, 3]], 4, 是, all_parent_open_intersections_normalized)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0012/)

子空間拓撲 · qf-mod39-subtop-induced-topology · candidate





## 13. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-induced-topology；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3],[0,1,2,3,4],[0,1,3],[0,3]],"subset":[2,3,4]}。請依 [subset, induced_topology, open_count, topology_certificate, certificate] 欄序回答。

查看答案與解釋([2, 3, 4], [[], [2, 3], [2, 3, 4], [3]], 4, 是, all_parent_open_intersections_normalized)

Wave6第二層核對=([2, 3, 4], [[], [2, 3], [2, 3, 4], [3]], 4, 是, all_parent_open_intersections_normalized)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0013/)

子空間拓撲 · qf-mod39-subtop-induced-topology · candidate





## 14. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-induced-topology；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,3],[0,1,3,4],[0,3]],"subset":[2,3,4]}。請依 [subset, induced_topology, open_count, topology_certificate, certificate] 欄序回答。

查看答案與解釋([2, 3, 4], [[], [2, 3, 4], [3], [3, 4]], 4, 是, all_parent_open_intersections_normalized)

Wave6第二層核對=([2, 3, 4], [[], [2, 3, 4], [3], [3, 4]], 4, 是, all_parent_open_intersections_normalized)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0014/)

子空間拓撲 · qf-mod39-subtop-induced-topology · candidate





## 15. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-induced-topology；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3],[0,1,2,3,4],[0,2,3],[0,3]],"subset":[1,3,4]}。請依 [subset, induced_topology, open_count, topology_certificate, certificate] 欄序回答。

查看答案與解釋([1, 3, 4], [[], [1, 3], [1, 3, 4], [3]], 4, 是, all_parent_open_intersections_normalized)

Wave6第二層核對=([1, 3, 4], [[], [1, 3], [1, 3, 4], [3]], 4, 是, all_parent_open_intersections_normalized)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0015/)

子空間拓撲 · qf-mod39-subtop-induced-topology · candidate





## 16. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-induced-topology；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2,3],[0,2,3,4],[0,3]],"subset":[1,3,4]}。請依 [subset, induced_topology, open_count, topology_certificate, certificate] 欄序回答。

查看答案與解釋([1, 3, 4], [[], [1, 3, 4], [3], [3, 4]], 4, 是, all_parent_open_intersections_normalized)

Wave6第二層核對=([1, 3, 4], [[], [1, 3, 4], [3], [3, 4]], 4, 是, all_parent_open_intersections_normalized)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0016/)

子空間拓撲 · qf-mod39-subtop-induced-topology · candidate





## 17. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-induced-topology；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,3,4],[0,3],[0,3,4]],"subset":[1,2,3]}。請依 [subset, induced_topology, open_count, topology_certificate, certificate] 欄序回答。

查看答案與解釋([1, 2, 3], [[], [1, 2, 3], [1, 3], [3]], 4, 是, all_parent_open_intersections_normalized)

Wave6第二層核對=([1, 2, 3], [[], [1, 2, 3], [1, 3], [3]], 4, 是, all_parent_open_intersections_normalized)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0017/)

子空間拓撲 · qf-mod39-subtop-induced-topology · candidate





## 18. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-induced-topology；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2,3,4],[0,3],[0,3,4]],"subset":[1,2,3]}。請依 [subset, induced_topology, open_count, topology_certificate, certificate] 欄序回答。

查看答案與解釋([1, 2, 3], [[], [1, 2, 3], [2, 3], [3]], 4, 是, all_parent_open_intersections_normalized)

Wave6第二層核對=([1, 2, 3], [[], [1, 2, 3], [2, 3], [3]], 4, 是, all_parent_open_intersections_normalized)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0018/)

子空間拓撲 · qf-mod39-subtop-induced-topology · candidate





## 19. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-induced-topology；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,2,4],[0,1,4],[0,4]],"subset":[2,3,4]}。請依 [subset, induced_topology, open_count, topology_certificate, certificate] 欄序回答。

查看答案與解釋([2, 3, 4], [[], [2, 3, 4], [2, 4], [4]], 4, 是, all_parent_open_intersections_normalized)

Wave6第二層核對=([2, 3, 4], [[], [2, 3, 4], [2, 4], [4]], 4, 是, all_parent_open_intersections_normalized)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0019/)

子空間拓撲 · qf-mod39-subtop-induced-topology · candidate





## 20. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-induced-topology；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,3,4],[0,1,4],[0,4]],"subset":[2,3,4]}。請依 [subset, induced_topology, open_count, topology_certificate, certificate] 欄序回答。

查看答案與解釋([2, 3, 4], [[], [2, 3, 4], [3, 4], [4]], 4, 是, all_parent_open_intersections_normalized)

Wave6第二層核對=([2, 3, 4], [[], [2, 3, 4], [3, 4], [4]], 4, 是, all_parent_open_intersections_normalized)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0020/)

子空間拓撲 · qf-mod39-subtop-induced-topology · candidate





## 21. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-induced-topology；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,2,4],[0,2,4],[0,4]],"subset":[1,3,4]}。請依 [subset, induced_topology, open_count, topology_certificate, certificate] 欄序回答。

查看答案與解釋([1, 3, 4], [[], [1, 3, 4], [1, 4], [4]], 4, 是, all_parent_open_intersections_normalized)

Wave6第二層核對=([1, 3, 4], [[], [1, 3, 4], [1, 4], [4]], 4, 是, all_parent_open_intersections_normalized)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0021/)

子空間拓撲 · qf-mod39-subtop-induced-topology · candidate





## 22. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-induced-topology；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2,3,4],[0,2,4],[0,4]],"subset":[1,3,4]}。請依 [subset, induced_topology, open_count, topology_certificate, certificate] 欄序回答。

查看答案與解釋([1, 3, 4], [[], [1, 3, 4], [3, 4], [4]], 4, 是, all_parent_open_intersections_normalized)

Wave6第二層核對=([1, 3, 4], [[], [1, 3, 4], [3, 4], [4]], 4, 是, all_parent_open_intersections_normalized)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0022/)

子空間拓撲 · qf-mod39-subtop-induced-topology · candidate





## 23. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-induced-topology；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,3,4],[0,3,4],[0,4]],"subset":[1,2,4]}。請依 [subset, induced_topology, open_count, topology_certificate, certificate] 欄序回答。

查看答案與解釋([1, 2, 4], [[], [1, 2, 4], [1, 4], [4]], 4, 是, all_parent_open_intersections_normalized)

Wave6第二層核對=([1, 2, 4], [[], [1, 2, 4], [1, 4], [4]], 4, 是, all_parent_open_intersections_normalized)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0023/)

子空間拓撲 · qf-mod39-subtop-induced-topology · candidate





## 24. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-induced-topology；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2,3,4],[0,3,4],[0,4]],"subset":[1,2,4]}。請依 [subset, induced_topology, open_count, topology_certificate, certificate] 欄序回答。

查看答案與解釋([1, 2, 4], [[], [1, 2, 4], [2, 4], [4]], 4, 是, all_parent_open_intersections_normalized)

Wave6第二層核對=([1, 2, 4], [[], [1, 2, 4], [2, 4], [4]], 4, 是, all_parent_open_intersections_normalized)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0024/)

子空間拓撲 · qf-mod39-subtop-induced-topology · candidate





## 25. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-induced-topology；資料={"n":5,"parent_topology":[[],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[1]],"subset":[0,3,4]}。請依 [subset, induced_topology, open_count, topology_certificate, certificate] 欄序回答。

查看答案與解釋([0, 3, 4], [[], [0], [0, 3], [0, 3, 4]], 4, 是, all_parent_open_intersections_normalized)

Wave6第二層核對=([0, 3, 4], [[], [0], [0, 3], [0, 3, 4]], 4, 是, all_parent_open_intersections_normalized)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0025/)

子空間拓撲 · qf-mod39-subtop-induced-topology · candidate





## 26. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-open-audit；資料={"n":5,"parent_topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4]],"subset":[1,3,4],"candidate":[1]}。請依 [candidate, relative_open, parent_open_witnesses, boundary] 欄序回答。

查看答案與解釋([1], 是, [[0, 1], [0, 1, 2]], relative_open_need_not_be_ambient_open)

Wave6第二層核對=([1], 是, [[0, 1], [0, 1, 2]], relative_open_need_not_be_ambient_open)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0026/)

子空間拓撲 · qf-mod39-subtop-relative-open-audit · candidate





## 27. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-open-audit；資料={"n":5,"parent_topology":[[],[0],[0,1],[0,1,2],[0,1,2,3,4],[0,1,2,4]],"subset":[1,3,4],"candidate":[1]}。請依 [candidate, relative_open, parent_open_witnesses, boundary] 欄序回答。

查看答案與解釋([1], 是, [[0, 1], [0, 1, 2]], relative_open_need_not_be_ambient_open)

Wave6第二層核對=([1], 是, [[0, 1], [0, 1, 2]], relative_open_need_not_be_ambient_open)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0027/)

子空間拓撲 · qf-mod39-subtop-relative-open-audit · candidate





## 28. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-open-audit；資料={"n":5,"parent_topology":[[],[0],[0,1],[0,1,2,3],[0,1,2,3,4],[0,1,3]],"subset":[1,2,4],"candidate":[1]}。請依 [candidate, relative_open, parent_open_witnesses, boundary] 欄序回答。

查看答案與解釋([1], 是, [[0, 1], [0, 1, 3]], relative_open_need_not_be_ambient_open)

Wave6第二層核對=([1], 是, [[0, 1], [0, 1, 3]], relative_open_need_not_be_ambient_open)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0028/)

子空間拓撲 · qf-mod39-subtop-relative-open-audit · candidate





## 29. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-open-audit；資料={"n":5,"parent_topology":[[],[0],[0,1],[0,1,2,3,4],[0,1,3],[0,1,3,4]],"subset":[1,2,4],"candidate":[1]}。請依 [candidate, relative_open, parent_open_witnesses, boundary] 欄序回答。

查看答案與解釋([1], 是, [[0, 1], [0, 1, 3]], relative_open_need_not_be_ambient_open)

Wave6第二層核對=([1], 是, [[0, 1], [0, 1, 3]], relative_open_need_not_be_ambient_open)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0029/)

子空間拓撲 · qf-mod39-subtop-relative-open-audit · candidate





## 30. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-open-audit；資料={"n":5,"parent_topology":[[],[0],[0,1],[0,1,2,3,4],[0,1,2,4],[0,1,4]],"subset":[1,2,3],"candidate":[1]}。請依 [candidate, relative_open, parent_open_witnesses, boundary] 欄序回答。

查看答案與解釋([1], 是, [[0, 1], [0, 1, 4]], relative_open_need_not_be_ambient_open)

Wave6第二層核對=([1], 是, [[0, 1], [0, 1, 4]], relative_open_need_not_be_ambient_open)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0030/)

子空間拓撲 · qf-mod39-subtop-relative-open-audit · candidate





## 31. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-open-audit；資料={"n":5,"parent_topology":[[],[0],[0,1],[0,1,2,3,4],[0,1,3,4],[0,1,4]],"subset":[1,2,3],"candidate":[1]}。請依 [candidate, relative_open, parent_open_witnesses, boundary] 欄序回答。

查看答案與解釋([1], 是, [[0, 1], [0, 1, 4]], relative_open_need_not_be_ambient_open)

Wave6第二層核對=([1], 是, [[0, 1], [0, 1, 4]], relative_open_need_not_be_ambient_open)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0031/)

子空間拓撲 · qf-mod39-subtop-relative-open-audit · candidate





## 32. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-open-audit；資料={"n":5,"parent_topology":[[],[0],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,2]],"subset":[2,3,4],"candidate":[2]}。請依 [candidate, relative_open, parent_open_witnesses, boundary] 欄序回答。

查看答案與解釋([2], 是, [[0, 1, 2], [0, 2]], relative_open_need_not_be_ambient_open)

Wave6第二層核對=([2], 是, [[0, 1, 2], [0, 2]], relative_open_need_not_be_ambient_open)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0032/)

子空間拓撲 · qf-mod39-subtop-relative-open-audit · candidate





## 33. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-open-audit；資料={"n":5,"parent_topology":[[],[0],[0,1,2],[0,1,2,3,4],[0,1,2,4],[0,2]],"subset":[2,3,4],"candidate":[2]}。請依 [candidate, relative_open, parent_open_witnesses, boundary] 欄序回答。

查看答案與解釋([2], 是, [[0, 1, 2], [0, 2]], relative_open_need_not_be_ambient_open)

Wave6第二層核對=([2], 是, [[0, 1, 2], [0, 2]], relative_open_need_not_be_ambient_open)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0033/)

子空間拓撲 · qf-mod39-subtop-relative-open-audit · candidate





## 34. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-open-audit；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3],[0,1,2,3,4],[0,2],[0,2,3]],"subset":[1,2,4],"candidate":[2]}。請依 [candidate, relative_open, parent_open_witnesses, boundary] 欄序回答。

查看答案與解釋([2], 是, [[0, 2], [0, 2, 3]], relative_open_need_not_be_ambient_open)

Wave6第二層核對=([2], 是, [[0, 2], [0, 2, 3]], relative_open_need_not_be_ambient_open)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0034/)

子空間拓撲 · qf-mod39-subtop-relative-open-audit · candidate





## 35. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-open-audit；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2],[0,2,3],[0,2,3,4]],"subset":[1,2,4],"candidate":[2]}。請依 [candidate, relative_open, parent_open_witnesses, boundary] 欄序回答。

查看答案與解釋([2], 是, [[0, 2], [0, 2, 3]], relative_open_need_not_be_ambient_open)

Wave6第二層核對=([2], 是, [[0, 2], [0, 2, 3]], relative_open_need_not_be_ambient_open)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0035/)

子空間拓撲 · qf-mod39-subtop-relative-open-audit · candidate





## 36. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-open-audit；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,2,4],[0,2],[0,2,4]],"subset":[1,2,3],"candidate":[2]}。請依 [candidate, relative_open, parent_open_witnesses, boundary] 欄序回答。

查看答案與解釋([2], 是, [[0, 2], [0, 2, 4]], relative_open_need_not_be_ambient_open)

Wave6第二層核對=([2], 是, [[0, 2], [0, 2, 4]], relative_open_need_not_be_ambient_open)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0036/)

子空間拓撲 · qf-mod39-subtop-relative-open-audit · candidate





## 37. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-open-audit；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2],[0,2,3,4],[0,2,4]],"subset":[1,2,3],"candidate":[2]}。請依 [candidate, relative_open, parent_open_witnesses, boundary] 欄序回答。

查看答案與解釋([2], 是, [[0, 2], [0, 2, 4]], relative_open_need_not_be_ambient_open)

Wave6第二層核對=([2], 是, [[0, 2], [0, 2, 4]], relative_open_need_not_be_ambient_open)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0037/)

子空間拓撲 · qf-mod39-subtop-relative-open-audit · candidate





## 38. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-open-audit；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3],[0,1,2,3,4],[0,1,3],[0,3]],"subset":[2,3,4],"candidate":[3]}。請依 [candidate, relative_open, parent_open_witnesses, boundary] 欄序回答。

查看答案與解釋([3], 是, [[0, 1, 3], [0, 3]], relative_open_need_not_be_ambient_open)

Wave6第二層核對=([3], 是, [[0, 1, 3], [0, 3]], relative_open_need_not_be_ambient_open)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0038/)

子空間拓撲 · qf-mod39-subtop-relative-open-audit · candidate





## 39. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-open-audit；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,3],[0,1,3,4],[0,3]],"subset":[2,3,4],"candidate":[3]}。請依 [candidate, relative_open, parent_open_witnesses, boundary] 欄序回答。

查看答案與解釋([3], 是, [[0, 1, 3], [0, 3]], relative_open_need_not_be_ambient_open)

Wave6第二層核對=([3], 是, [[0, 1, 3], [0, 3]], relative_open_need_not_be_ambient_open)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0039/)

子空間拓撲 · qf-mod39-subtop-relative-open-audit · candidate





## 40. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-open-audit；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3],[0,1,2,3,4],[0,2,3],[0,3]],"subset":[1,3,4],"candidate":[3]}。請依 [candidate, relative_open, parent_open_witnesses, boundary] 欄序回答。

查看答案與解釋([3], 是, [[0, 2, 3], [0, 3]], relative_open_need_not_be_ambient_open)

Wave6第二層核對=([3], 是, [[0, 2, 3], [0, 3]], relative_open_need_not_be_ambient_open)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0040/)

子空間拓撲 · qf-mod39-subtop-relative-open-audit · candidate





## 41. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-open-audit；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2,3],[0,2,3,4],[0,3]],"subset":[1,3,4],"candidate":[3]}。請依 [candidate, relative_open, parent_open_witnesses, boundary] 欄序回答。

查看答案與解釋([3], 是, [[0, 2, 3], [0, 3]], relative_open_need_not_be_ambient_open)

Wave6第二層核對=([3], 是, [[0, 2, 3], [0, 3]], relative_open_need_not_be_ambient_open)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0041/)

子空間拓撲 · qf-mod39-subtop-relative-open-audit · candidate





## 42. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-open-audit；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,3,4],[0,3],[0,3,4]],"subset":[1,2,3],"candidate":[3]}。請依 [candidate, relative_open, parent_open_witnesses, boundary] 欄序回答。

查看答案與解釋([3], 是, [[0, 3], [0, 3, 4]], relative_open_need_not_be_ambient_open)

Wave6第二層核對=([3], 是, [[0, 3], [0, 3, 4]], relative_open_need_not_be_ambient_open)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0042/)

子空間拓撲 · qf-mod39-subtop-relative-open-audit · candidate





## 43. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-open-audit；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2,3,4],[0,3],[0,3,4]],"subset":[1,2,3],"candidate":[3]}。請依 [candidate, relative_open, parent_open_witnesses, boundary] 欄序回答。

查看答案與解釋([3], 是, [[0, 3], [0, 3, 4]], relative_open_need_not_be_ambient_open)

Wave6第二層核對=([3], 是, [[0, 3], [0, 3, 4]], relative_open_need_not_be_ambient_open)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0043/)

子空間拓撲 · qf-mod39-subtop-relative-open-audit · candidate





## 44. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-open-audit；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,2,4],[0,1,4],[0,4]],"subset":[2,3,4],"candidate":[4]}。請依 [candidate, relative_open, parent_open_witnesses, boundary] 欄序回答。

查看答案與解釋([4], 是, [[0, 1, 4], [0, 4]], relative_open_need_not_be_ambient_open)

Wave6第二層核對=([4], 是, [[0, 1, 4], [0, 4]], relative_open_need_not_be_ambient_open)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0044/)

子空間拓撲 · qf-mod39-subtop-relative-open-audit · candidate





## 45. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-open-audit；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,3,4],[0,1,4],[0,4]],"subset":[2,3,4],"candidate":[4]}。請依 [candidate, relative_open, parent_open_witnesses, boundary] 欄序回答。

查看答案與解釋([4], 是, [[0, 1, 4], [0, 4]], relative_open_need_not_be_ambient_open)

Wave6第二層核對=([4], 是, [[0, 1, 4], [0, 4]], relative_open_need_not_be_ambient_open)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0045/)

子空間拓撲 · qf-mod39-subtop-relative-open-audit · candidate





## 46. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-open-audit；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,2,4],[0,2,4],[0,4]],"subset":[1,3,4],"candidate":[4]}。請依 [candidate, relative_open, parent_open_witnesses, boundary] 欄序回答。

查看答案與解釋([4], 是, [[0, 2, 4], [0, 4]], relative_open_need_not_be_ambient_open)

Wave6第二層核對=([4], 是, [[0, 2, 4], [0, 4]], relative_open_need_not_be_ambient_open)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0046/)

子空間拓撲 · qf-mod39-subtop-relative-open-audit · candidate





## 47. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-open-audit；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2,3,4],[0,2,4],[0,4]],"subset":[1,3,4],"candidate":[4]}。請依 [candidate, relative_open, parent_open_witnesses, boundary] 欄序回答。

查看答案與解釋([4], 是, [[0, 2, 4], [0, 4]], relative_open_need_not_be_ambient_open)

Wave6第二層核對=([4], 是, [[0, 2, 4], [0, 4]], relative_open_need_not_be_ambient_open)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0047/)

子空間拓撲 · qf-mod39-subtop-relative-open-audit · candidate





## 48. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-open-audit；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,3,4],[0,3,4],[0,4]],"subset":[1,2,4],"candidate":[4]}。請依 [candidate, relative_open, parent_open_witnesses, boundary] 欄序回答。

查看答案與解釋([4], 是, [[0, 3, 4], [0, 4]], relative_open_need_not_be_ambient_open)

Wave6第二層核對=([4], 是, [[0, 3, 4], [0, 4]], relative_open_need_not_be_ambient_open)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0048/)

子空間拓撲 · qf-mod39-subtop-relative-open-audit · candidate





## 49. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-open-audit；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2,3,4],[0,3,4],[0,4]],"subset":[1,2,4],"candidate":[4]}。請依 [candidate, relative_open, parent_open_witnesses, boundary] 欄序回答。

查看答案與解釋([4], 是, [[0, 3, 4], [0, 4]], relative_open_need_not_be_ambient_open)

Wave6第二層核對=([4], 是, [[0, 3, 4], [0, 4]], relative_open_need_not_be_ambient_open)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0049/)

子空間拓撲 · qf-mod39-subtop-relative-open-audit · candidate





## 50. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-open-audit；資料={"n":5,"parent_topology":[[],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[1]],"subset":[0,3,4],"candidate":[0]}。請依 [candidate, relative_open, parent_open_witnesses, boundary] 欄序回答。

查看答案與解釋([0], 是, [[0, 1], [0, 1, 2]], relative_open_need_not_be_ambient_open)

Wave6第二層核對=([0], 是, [[0, 1], [0, 1, 2]], relative_open_need_not_be_ambient_open)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0050/)

子空間拓撲 · qf-mod39-subtop-relative-open-audit · candidate





## 51. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-closed-audit；資料={"n":5,"parent_topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4]],"subset":[1,3,4],"candidate":[3,4]}。請依 [candidate, relative_complement, relative_closed, boundary] 欄序回答。

relative_complement在Y內取，不是在母空間X內取。

查看答案與解釋([3, 4], [1], 是, complement_taken_inside_Y)

Wave6第二層核對=([3, 4], [1], 是, complement_taken_inside_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0051/)

子空間拓撲 · qf-mod39-subtop-relative-closed-audit · candidate





## 52. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-closed-audit；資料={"n":5,"parent_topology":[[],[0],[0,1],[0,1,2],[0,1,2,3,4],[0,1,2,4]],"subset":[1,3,4],"candidate":[3,4]}。請依 [candidate, relative_complement, relative_closed, boundary] 欄序回答。

relative_complement在Y內取，不是在母空間X內取。

查看答案與解釋([3, 4], [1], 是, complement_taken_inside_Y)

Wave6第二層核對=([3, 4], [1], 是, complement_taken_inside_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0052/)

子空間拓撲 · qf-mod39-subtop-relative-closed-audit · candidate





## 53. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-closed-audit；資料={"n":5,"parent_topology":[[],[0],[0,1],[0,1,2,3],[0,1,2,3,4],[0,1,3]],"subset":[1,2,4],"candidate":[2,4]}。請依 [candidate, relative_complement, relative_closed, boundary] 欄序回答。

relative_complement在Y內取，不是在母空間X內取。

查看答案與解釋([2, 4], [1], 是, complement_taken_inside_Y)

Wave6第二層核對=([2, 4], [1], 是, complement_taken_inside_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0053/)

子空間拓撲 · qf-mod39-subtop-relative-closed-audit · candidate





## 54. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-closed-audit；資料={"n":5,"parent_topology":[[],[0],[0,1],[0,1,2,3,4],[0,1,3],[0,1,3,4]],"subset":[1,2,4],"candidate":[2,4]}。請依 [candidate, relative_complement, relative_closed, boundary] 欄序回答。

relative_complement在Y內取，不是在母空間X內取。

查看答案與解釋([2, 4], [1], 是, complement_taken_inside_Y)

Wave6第二層核對=([2, 4], [1], 是, complement_taken_inside_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0054/)

子空間拓撲 · qf-mod39-subtop-relative-closed-audit · candidate





## 55. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-closed-audit；資料={"n":5,"parent_topology":[[],[0],[0,1],[0,1,2,3,4],[0,1,2,4],[0,1,4]],"subset":[1,2,3],"candidate":[2,3]}。請依 [candidate, relative_complement, relative_closed, boundary] 欄序回答。

relative_complement在Y內取，不是在母空間X內取。

查看答案與解釋([2, 3], [1], 是, complement_taken_inside_Y)

Wave6第二層核對=([2, 3], [1], 是, complement_taken_inside_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0055/)

子空間拓撲 · qf-mod39-subtop-relative-closed-audit · candidate





## 56. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-closed-audit；資料={"n":5,"parent_topology":[[],[0],[0,1],[0,1,2,3,4],[0,1,3,4],[0,1,4]],"subset":[1,2,3],"candidate":[2,3]}。請依 [candidate, relative_complement, relative_closed, boundary] 欄序回答。

relative_complement在Y內取，不是在母空間X內取。

查看答案與解釋([2, 3], [1], 是, complement_taken_inside_Y)

Wave6第二層核對=([2, 3], [1], 是, complement_taken_inside_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0056/)

子空間拓撲 · qf-mod39-subtop-relative-closed-audit · candidate





## 57. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-closed-audit；資料={"n":5,"parent_topology":[[],[0],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,2]],"subset":[2,3,4],"candidate":[3,4]}。請依 [candidate, relative_complement, relative_closed, boundary] 欄序回答。

relative_complement在Y內取，不是在母空間X內取。

查看答案與解釋([3, 4], [2], 是, complement_taken_inside_Y)

Wave6第二層核對=([3, 4], [2], 是, complement_taken_inside_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0057/)

子空間拓撲 · qf-mod39-subtop-relative-closed-audit · candidate





## 58. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-closed-audit；資料={"n":5,"parent_topology":[[],[0],[0,1,2],[0,1,2,3,4],[0,1,2,4],[0,2]],"subset":[2,3,4],"candidate":[3,4]}。請依 [candidate, relative_complement, relative_closed, boundary] 欄序回答。

relative_complement在Y內取，不是在母空間X內取。

查看答案與解釋([3, 4], [2], 是, complement_taken_inside_Y)

Wave6第二層核對=([3, 4], [2], 是, complement_taken_inside_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0058/)

子空間拓撲 · qf-mod39-subtop-relative-closed-audit · candidate





## 59. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-closed-audit；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3],[0,1,2,3,4],[0,2],[0,2,3]],"subset":[1,2,4],"candidate":[1,4]}。請依 [candidate, relative_complement, relative_closed, boundary] 欄序回答。

relative_complement在Y內取，不是在母空間X內取。

查看答案與解釋([1, 4], [2], 是, complement_taken_inside_Y)

Wave6第二層核對=([1, 4], [2], 是, complement_taken_inside_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0059/)

子空間拓撲 · qf-mod39-subtop-relative-closed-audit · candidate





## 60. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-closed-audit；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2],[0,2,3],[0,2,3,4]],"subset":[1,2,4],"candidate":[1,4]}。請依 [candidate, relative_complement, relative_closed, boundary] 欄序回答。

relative_complement在Y內取，不是在母空間X內取。

查看答案與解釋([1, 4], [2], 是, complement_taken_inside_Y)

Wave6第二層核對=([1, 4], [2], 是, complement_taken_inside_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0060/)

子空間拓撲 · qf-mod39-subtop-relative-closed-audit · candidate





## 61. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-closed-audit；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,2,4],[0,2],[0,2,4]],"subset":[1,2,3],"candidate":[1,3]}。請依 [candidate, relative_complement, relative_closed, boundary] 欄序回答。

relative_complement在Y內取，不是在母空間X內取。

查看答案與解釋([1, 3], [2], 是, complement_taken_inside_Y)

Wave6第二層核對=([1, 3], [2], 是, complement_taken_inside_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0061/)

子空間拓撲 · qf-mod39-subtop-relative-closed-audit · candidate





## 62. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-closed-audit；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2],[0,2,3,4],[0,2,4]],"subset":[1,2,3],"candidate":[1,3]}。請依 [candidate, relative_complement, relative_closed, boundary] 欄序回答。

relative_complement在Y內取，不是在母空間X內取。

查看答案與解釋([1, 3], [2], 是, complement_taken_inside_Y)

Wave6第二層核對=([1, 3], [2], 是, complement_taken_inside_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0062/)

子空間拓撲 · qf-mod39-subtop-relative-closed-audit · candidate





## 63. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-closed-audit；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3],[0,1,2,3,4],[0,1,3],[0,3]],"subset":[2,3,4],"candidate":[2,4]}。請依 [candidate, relative_complement, relative_closed, boundary] 欄序回答。

relative_complement在Y內取，不是在母空間X內取。

查看答案與解釋([2, 4], [3], 是, complement_taken_inside_Y)

Wave6第二層核對=([2, 4], [3], 是, complement_taken_inside_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0063/)

子空間拓撲 · qf-mod39-subtop-relative-closed-audit · candidate





## 64. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-closed-audit；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,3],[0,1,3,4],[0,3]],"subset":[2,3,4],"candidate":[2,4]}。請依 [candidate, relative_complement, relative_closed, boundary] 欄序回答。

relative_complement在Y內取，不是在母空間X內取。

查看答案與解釋([2, 4], [3], 是, complement_taken_inside_Y)

Wave6第二層核對=([2, 4], [3], 是, complement_taken_inside_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0064/)

子空間拓撲 · qf-mod39-subtop-relative-closed-audit · candidate





## 65. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-closed-audit；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3],[0,1,2,3,4],[0,2,3],[0,3]],"subset":[1,3,4],"candidate":[1,4]}。請依 [candidate, relative_complement, relative_closed, boundary] 欄序回答。

relative_complement在Y內取，不是在母空間X內取。

查看答案與解釋([1, 4], [3], 是, complement_taken_inside_Y)

Wave6第二層核對=([1, 4], [3], 是, complement_taken_inside_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0065/)

子空間拓撲 · qf-mod39-subtop-relative-closed-audit · candidate





## 66. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-closed-audit；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2,3],[0,2,3,4],[0,3]],"subset":[1,3,4],"candidate":[1,4]}。請依 [candidate, relative_complement, relative_closed, boundary] 欄序回答。

relative_complement在Y內取，不是在母空間X內取。

查看答案與解釋([1, 4], [3], 是, complement_taken_inside_Y)

Wave6第二層核對=([1, 4], [3], 是, complement_taken_inside_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0066/)

子空間拓撲 · qf-mod39-subtop-relative-closed-audit · candidate





## 67. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-closed-audit；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,3,4],[0,3],[0,3,4]],"subset":[1,2,3],"candidate":[1,2]}。請依 [candidate, relative_complement, relative_closed, boundary] 欄序回答。

relative_complement在Y內取，不是在母空間X內取。

查看答案與解釋([1, 2], [3], 是, complement_taken_inside_Y)

Wave6第二層核對=([1, 2], [3], 是, complement_taken_inside_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0067/)

子空間拓撲 · qf-mod39-subtop-relative-closed-audit · candidate





## 68. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-closed-audit；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2,3,4],[0,3],[0,3,4]],"subset":[1,2,3],"candidate":[1,2]}。請依 [candidate, relative_complement, relative_closed, boundary] 欄序回答。

relative_complement在Y內取，不是在母空間X內取。

查看答案與解釋([1, 2], [3], 是, complement_taken_inside_Y)

Wave6第二層核對=([1, 2], [3], 是, complement_taken_inside_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0068/)

子空間拓撲 · qf-mod39-subtop-relative-closed-audit · candidate





## 69. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-closed-audit；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,2,4],[0,1,4],[0,4]],"subset":[2,3,4],"candidate":[2,3]}。請依 [candidate, relative_complement, relative_closed, boundary] 欄序回答。

relative_complement在Y內取，不是在母空間X內取。

查看答案與解釋([2, 3], [4], 是, complement_taken_inside_Y)

Wave6第二層核對=([2, 3], [4], 是, complement_taken_inside_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0069/)

子空間拓撲 · qf-mod39-subtop-relative-closed-audit · candidate





## 70. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-closed-audit；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,3,4],[0,1,4],[0,4]],"subset":[2,3,4],"candidate":[2,3]}。請依 [candidate, relative_complement, relative_closed, boundary] 欄序回答。

relative_complement在Y內取，不是在母空間X內取。

查看答案與解釋([2, 3], [4], 是, complement_taken_inside_Y)

Wave6第二層核對=([2, 3], [4], 是, complement_taken_inside_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0070/)

子空間拓撲 · qf-mod39-subtop-relative-closed-audit · candidate





## 71. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-closed-audit；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,2,4],[0,2,4],[0,4]],"subset":[1,3,4],"candidate":[1,3]}。請依 [candidate, relative_complement, relative_closed, boundary] 欄序回答。

relative_complement在Y內取，不是在母空間X內取。

查看答案與解釋([1, 3], [4], 是, complement_taken_inside_Y)

Wave6第二層核對=([1, 3], [4], 是, complement_taken_inside_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0071/)

子空間拓撲 · qf-mod39-subtop-relative-closed-audit · candidate





## 72. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-closed-audit；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2,3,4],[0,2,4],[0,4]],"subset":[1,3,4],"candidate":[1,3]}。請依 [candidate, relative_complement, relative_closed, boundary] 欄序回答。

relative_complement在Y內取，不是在母空間X內取。

查看答案與解釋([1, 3], [4], 是, complement_taken_inside_Y)

Wave6第二層核對=([1, 3], [4], 是, complement_taken_inside_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0072/)

子空間拓撲 · qf-mod39-subtop-relative-closed-audit · candidate





## 73. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-closed-audit；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,3,4],[0,3,4],[0,4]],"subset":[1,2,4],"candidate":[1,2]}。請依 [candidate, relative_complement, relative_closed, boundary] 欄序回答。

relative_complement在Y內取，不是在母空間X內取。

查看答案與解釋([1, 2], [4], 是, complement_taken_inside_Y)

Wave6第二層核對=([1, 2], [4], 是, complement_taken_inside_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0073/)

子空間拓撲 · qf-mod39-subtop-relative-closed-audit · candidate





## 74. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-closed-audit；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2,3,4],[0,3,4],[0,4]],"subset":[1,2,4],"candidate":[1,2]}。請依 [candidate, relative_complement, relative_closed, boundary] 欄序回答。

relative_complement在Y內取，不是在母空間X內取。

查看答案與解釋([1, 2], [4], 是, complement_taken_inside_Y)

Wave6第二層核對=([1, 2], [4], 是, complement_taken_inside_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0074/)

子空間拓撲 · qf-mod39-subtop-relative-closed-audit · candidate





## 75. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-closed-audit；資料={"n":5,"parent_topology":[[],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[1]],"subset":[0,3,4],"candidate":[3,4]}。請依 [candidate, relative_complement, relative_closed, boundary] 欄序回答。

relative_complement在Y內取，不是在母空間X內取。

查看答案與解釋([3, 4], [0], 是, complement_taken_inside_Y)

Wave6第二層核對=([3, 4], [0], 是, complement_taken_inside_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0075/)

子空間拓撲 · qf-mod39-subtop-relative-closed-audit · candidate





## 76. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-ambient-boundary；資料={"n":5,"parent_topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4]],"subset":[1,3,4],"candidate":[1,3,4]}。請依 [candidate, relative_open, ambient_open, intersection_certificate, boundary] 欄序回答。

查看答案與解釋([1, 3, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)

Wave6第二層核對=([1, 3, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0076/)

子空間拓撲 · qf-mod39-subtop-ambient-boundary · candidate





## 77. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-ambient-boundary；資料={"n":5,"parent_topology":[[],[0],[0,1],[0,1,2],[0,1,2,3,4],[0,1,2,4]],"subset":[1,3,4],"candidate":[1,3,4]}。請依 [candidate, relative_open, ambient_open, intersection_certificate, boundary] 欄序回答。

查看答案與解釋([1, 3, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)

Wave6第二層核對=([1, 3, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0077/)

子空間拓撲 · qf-mod39-subtop-ambient-boundary · candidate





## 78. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-ambient-boundary；資料={"n":5,"parent_topology":[[],[0],[0,1],[0,1,2,3],[0,1,2,3,4],[0,1,3]],"subset":[1,2,4],"candidate":[1,2,4]}。請依 [candidate, relative_open, ambient_open, intersection_certificate, boundary] 欄序回答。

查看答案與解釋([1, 2, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)

Wave6第二層核對=([1, 2, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0078/)

子空間拓撲 · qf-mod39-subtop-ambient-boundary · candidate





## 79. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-ambient-boundary；資料={"n":5,"parent_topology":[[],[0],[0,1],[0,1,2,3,4],[0,1,3],[0,1,3,4]],"subset":[1,2,4],"candidate":[1,2,4]}。請依 [candidate, relative_open, ambient_open, intersection_certificate, boundary] 欄序回答。

查看答案與解釋([1, 2, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)

Wave6第二層核對=([1, 2, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0079/)

子空間拓撲 · qf-mod39-subtop-ambient-boundary · candidate





## 80. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-ambient-boundary；資料={"n":5,"parent_topology":[[],[0],[0,1],[0,1,2,3,4],[0,1,2,4],[0,1,4]],"subset":[1,2,3],"candidate":[1,2,3]}。請依 [candidate, relative_open, ambient_open, intersection_certificate, boundary] 欄序回答。

查看答案與解釋([1, 2, 3], 是, 否, 是, O_intersect_Y_not_O_subset_Y)

Wave6第二層核對=([1, 2, 3], 是, 否, 是, O_intersect_Y_not_O_subset_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0080/)

子空間拓撲 · qf-mod39-subtop-ambient-boundary · candidate





## 81. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-ambient-boundary；資料={"n":5,"parent_topology":[[],[0],[0,1],[0,1,2,3,4],[0,1,3,4],[0,1,4]],"subset":[1,2,3],"candidate":[1,2,3]}。請依 [candidate, relative_open, ambient_open, intersection_certificate, boundary] 欄序回答。

查看答案與解釋([1, 2, 3], 是, 否, 是, O_intersect_Y_not_O_subset_Y)

Wave6第二層核對=([1, 2, 3], 是, 否, 是, O_intersect_Y_not_O_subset_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0081/)

子空間拓撲 · qf-mod39-subtop-ambient-boundary · candidate





## 82. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-ambient-boundary；資料={"n":5,"parent_topology":[[],[0],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,2]],"subset":[2,3,4],"candidate":[2,3,4]}。請依 [candidate, relative_open, ambient_open, intersection_certificate, boundary] 欄序回答。

查看答案與解釋([2, 3, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)

Wave6第二層核對=([2, 3, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0082/)

子空間拓撲 · qf-mod39-subtop-ambient-boundary · candidate





## 83. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-ambient-boundary；資料={"n":5,"parent_topology":[[],[0],[0,1,2],[0,1,2,3,4],[0,1,2,4],[0,2]],"subset":[2,3,4],"candidate":[2,3,4]}。請依 [candidate, relative_open, ambient_open, intersection_certificate, boundary] 欄序回答。

查看答案與解釋([2, 3, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)

Wave6第二層核對=([2, 3, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0083/)

子空間拓撲 · qf-mod39-subtop-ambient-boundary · candidate





## 84. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-ambient-boundary；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3],[0,1,2,3,4],[0,2],[0,2,3]],"subset":[1,2,4],"candidate":[1,2,4]}。請依 [candidate, relative_open, ambient_open, intersection_certificate, boundary] 欄序回答。

查看答案與解釋([1, 2, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)

Wave6第二層核對=([1, 2, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0084/)

子空間拓撲 · qf-mod39-subtop-ambient-boundary · candidate





## 85. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-ambient-boundary；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2],[0,2,3],[0,2,3,4]],"subset":[1,2,4],"candidate":[1,2,4]}。請依 [candidate, relative_open, ambient_open, intersection_certificate, boundary] 欄序回答。

查看答案與解釋([1, 2, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)

Wave6第二層核對=([1, 2, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0085/)

子空間拓撲 · qf-mod39-subtop-ambient-boundary · candidate





## 86. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-ambient-boundary；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,2,4],[0,2],[0,2,4]],"subset":[1,2,3],"candidate":[1,2,3]}。請依 [candidate, relative_open, ambient_open, intersection_certificate, boundary] 欄序回答。

查看答案與解釋([1, 2, 3], 是, 否, 是, O_intersect_Y_not_O_subset_Y)

Wave6第二層核對=([1, 2, 3], 是, 否, 是, O_intersect_Y_not_O_subset_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0086/)

子空間拓撲 · qf-mod39-subtop-ambient-boundary · candidate





## 87. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-ambient-boundary；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2],[0,2,3,4],[0,2,4]],"subset":[1,2,3],"candidate":[1,2,3]}。請依 [candidate, relative_open, ambient_open, intersection_certificate, boundary] 欄序回答。

查看答案與解釋([1, 2, 3], 是, 否, 是, O_intersect_Y_not_O_subset_Y)

Wave6第二層核對=([1, 2, 3], 是, 否, 是, O_intersect_Y_not_O_subset_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0087/)

子空間拓撲 · qf-mod39-subtop-ambient-boundary · candidate





## 88. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-ambient-boundary；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3],[0,1,2,3,4],[0,1,3],[0,3]],"subset":[2,3,4],"candidate":[2,3,4]}。請依 [candidate, relative_open, ambient_open, intersection_certificate, boundary] 欄序回答。

查看答案與解釋([2, 3, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)

Wave6第二層核對=([2, 3, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0088/)

子空間拓撲 · qf-mod39-subtop-ambient-boundary · candidate





## 89. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-ambient-boundary；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,3],[0,1,3,4],[0,3]],"subset":[2,3,4],"candidate":[2,3,4]}。請依 [candidate, relative_open, ambient_open, intersection_certificate, boundary] 欄序回答。

查看答案與解釋([2, 3, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)

Wave6第二層核對=([2, 3, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0089/)

子空間拓撲 · qf-mod39-subtop-ambient-boundary · candidate





## 90. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-ambient-boundary；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3],[0,1,2,3,4],[0,2,3],[0,3]],"subset":[1,3,4],"candidate":[1,3,4]}。請依 [candidate, relative_open, ambient_open, intersection_certificate, boundary] 欄序回答。

查看答案與解釋([1, 3, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)

Wave6第二層核對=([1, 3, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0090/)

子空間拓撲 · qf-mod39-subtop-ambient-boundary · candidate





## 91. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-ambient-boundary；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2,3],[0,2,3,4],[0,3]],"subset":[1,3,4],"candidate":[1,3,4]}。請依 [candidate, relative_open, ambient_open, intersection_certificate, boundary] 欄序回答。

查看答案與解釋([1, 3, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)

Wave6第二層核對=([1, 3, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0091/)

子空間拓撲 · qf-mod39-subtop-ambient-boundary · candidate





## 92. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-ambient-boundary；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,3,4],[0,3],[0,3,4]],"subset":[1,2,3],"candidate":[1,2,3]}。請依 [candidate, relative_open, ambient_open, intersection_certificate, boundary] 欄序回答。

查看答案與解釋([1, 2, 3], 是, 否, 是, O_intersect_Y_not_O_subset_Y)

Wave6第二層核對=([1, 2, 3], 是, 否, 是, O_intersect_Y_not_O_subset_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0092/)

子空間拓撲 · qf-mod39-subtop-ambient-boundary · candidate





## 93. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-ambient-boundary；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2,3,4],[0,3],[0,3,4]],"subset":[1,2,3],"candidate":[1,2,3]}。請依 [candidate, relative_open, ambient_open, intersection_certificate, boundary] 欄序回答。

查看答案與解釋([1, 2, 3], 是, 否, 是, O_intersect_Y_not_O_subset_Y)

Wave6第二層核對=([1, 2, 3], 是, 否, 是, O_intersect_Y_not_O_subset_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0093/)

子空間拓撲 · qf-mod39-subtop-ambient-boundary · candidate





## 94. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-ambient-boundary；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,2,4],[0,1,4],[0,4]],"subset":[2,3,4],"candidate":[2,3,4]}。請依 [candidate, relative_open, ambient_open, intersection_certificate, boundary] 欄序回答。

查看答案與解釋([2, 3, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)

Wave6第二層核對=([2, 3, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0094/)

子空間拓撲 · qf-mod39-subtop-ambient-boundary · candidate





## 95. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-ambient-boundary；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,3,4],[0,1,4],[0,4]],"subset":[2,3,4],"candidate":[2,3,4]}。請依 [candidate, relative_open, ambient_open, intersection_certificate, boundary] 欄序回答。

查看答案與解釋([2, 3, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)

Wave6第二層核對=([2, 3, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0095/)

子空間拓撲 · qf-mod39-subtop-ambient-boundary · candidate





## 96. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-ambient-boundary；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,2,4],[0,2,4],[0,4]],"subset":[1,3,4],"candidate":[1,3,4]}。請依 [candidate, relative_open, ambient_open, intersection_certificate, boundary] 欄序回答。

查看答案與解釋([1, 3, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)

Wave6第二層核對=([1, 3, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0096/)

子空間拓撲 · qf-mod39-subtop-ambient-boundary · candidate





## 97. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-ambient-boundary；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2,3,4],[0,2,4],[0,4]],"subset":[1,3,4],"candidate":[1,3,4]}。請依 [candidate, relative_open, ambient_open, intersection_certificate, boundary] 欄序回答。

查看答案與解釋([1, 3, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)

Wave6第二層核對=([1, 3, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0097/)

子空間拓撲 · qf-mod39-subtop-ambient-boundary · candidate





## 98. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-ambient-boundary；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,3,4],[0,3,4],[0,4]],"subset":[1,2,4],"candidate":[1,2,4]}。請依 [candidate, relative_open, ambient_open, intersection_certificate, boundary] 欄序回答。

查看答案與解釋([1, 2, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)

Wave6第二層核對=([1, 2, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0098/)

子空間拓撲 · qf-mod39-subtop-ambient-boundary · candidate





## 99. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-ambient-boundary；資料={"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2,3,4],[0,3,4],[0,4]],"subset":[1,2,4],"candidate":[1,2,4]}。請依 [candidate, relative_open, ambient_open, intersection_certificate, boundary] 欄序回答。

查看答案與解釋([1, 2, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)

Wave6第二層核對=([1, 2, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0099/)

子空間拓撲 · qf-mod39-subtop-ambient-boundary · candidate





## 100. 子空間拓撲

完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-ambient-boundary；資料={"n":5,"parent_topology":[[],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[1]],"subset":[0,3,4],"candidate":[0,3,4]}。請依 [candidate, relative_open, ambient_open, intersection_certificate, boundary] 欄序回答。

查看答案與解釋([0, 3, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)

Wave6第二層核對=([0, 3, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r03-subspace-topology-0100/)

子空間拓撲 · qf-mod39-subtop-ambient-boundary · candidate



[原始題目 JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261014-advance-20261108-r03-subspace-topology-foundations/questions.jsonl) · [驗收報告](https://ocme.evemisslab.com/data/questions/batches/batch-20261014-advance-20261108-r03-subspace-topology-foundations/validation-report.json)