# 緊緻子集基礎 · 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-20261109-r03-compact-subset-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. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-finite-compactness；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, relative_open_count, compact, empty_subset, certificate] 欄序回答。

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

Wave6第三層核對=([1, 3, 4], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0001/)

緊緻子集 · qf-mod40-compact-finite-compactness · candidate





## 2. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-finite-compactness；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, relative_open_count, compact, empty_subset, certificate] 欄序回答。

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

Wave6第三層核對=([1, 3, 4], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0002/)

緊緻子集 · qf-mod40-compact-finite-compactness · candidate





## 3. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-finite-compactness；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, relative_open_count, compact, empty_subset, certificate] 欄序回答。

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

Wave6第三層核對=([1, 2, 4], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0003/)

緊緻子集 · qf-mod40-compact-finite-compactness · candidate





## 4. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-finite-compactness；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, relative_open_count, compact, empty_subset, certificate] 欄序回答。

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

Wave6第三層核對=([1, 2, 4], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0004/)

緊緻子集 · qf-mod40-compact-finite-compactness · candidate





## 5. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-finite-compactness；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, relative_open_count, compact, empty_subset, certificate] 欄序回答。

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

Wave6第三層核對=([1, 2, 3], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0005/)

緊緻子集 · qf-mod40-compact-finite-compactness · candidate





## 6. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-finite-compactness；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, relative_open_count, compact, empty_subset, certificate] 欄序回答。

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

Wave6第三層核對=([1, 2, 3], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0006/)

緊緻子集 · qf-mod40-compact-finite-compactness · candidate





## 7. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-finite-compactness；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, relative_open_count, compact, empty_subset, certificate] 欄序回答。

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

Wave6第三層核對=([2, 3, 4], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0007/)

緊緻子集 · qf-mod40-compact-finite-compactness · candidate





## 8. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-finite-compactness；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, relative_open_count, compact, empty_subset, certificate] 欄序回答。

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

Wave6第三層核對=([2, 3, 4], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0008/)

緊緻子集 · qf-mod40-compact-finite-compactness · candidate





## 9. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-finite-compactness；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, relative_open_count, compact, empty_subset, certificate] 欄序回答。

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

Wave6第三層核對=([1, 2, 4], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0009/)

緊緻子集 · qf-mod40-compact-finite-compactness · candidate





## 10. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-finite-compactness；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, relative_open_count, compact, empty_subset, certificate] 欄序回答。

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

Wave6第三層核對=([1, 2, 4], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0010/)

緊緻子集 · qf-mod40-compact-finite-compactness · candidate





## 11. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-finite-compactness；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, relative_open_count, compact, empty_subset, certificate] 欄序回答。

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

Wave6第三層核對=([1, 2, 3], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0011/)

緊緻子集 · qf-mod40-compact-finite-compactness · candidate





## 12. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-finite-compactness；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, relative_open_count, compact, empty_subset, certificate] 欄序回答。

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

Wave6第三層核對=([1, 2, 3], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0012/)

緊緻子集 · qf-mod40-compact-finite-compactness · candidate





## 13. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-finite-compactness；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, relative_open_count, compact, empty_subset, certificate] 欄序回答。

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

Wave6第三層核對=([2, 3, 4], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0013/)

緊緻子集 · qf-mod40-compact-finite-compactness · candidate





## 14. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-finite-compactness；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, relative_open_count, compact, empty_subset, certificate] 欄序回答。

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

Wave6第三層核對=([2, 3, 4], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0014/)

緊緻子集 · qf-mod40-compact-finite-compactness · candidate





## 15. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-finite-compactness；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, relative_open_count, compact, empty_subset, certificate] 欄序回答。

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

Wave6第三層核對=([1, 3, 4], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0015/)

緊緻子集 · qf-mod40-compact-finite-compactness · candidate





## 16. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-finite-compactness；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, relative_open_count, compact, empty_subset, certificate] 欄序回答。

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

Wave6第三層核對=([1, 3, 4], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0016/)

緊緻子集 · qf-mod40-compact-finite-compactness · candidate





## 17. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-finite-compactness；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, relative_open_count, compact, empty_subset, certificate] 欄序回答。

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

Wave6第三層核對=([1, 2, 3], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0017/)

緊緻子集 · qf-mod40-compact-finite-compactness · candidate





## 18. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-finite-compactness；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, relative_open_count, compact, empty_subset, certificate] 欄序回答。

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

Wave6第三層核對=([1, 2, 3], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0018/)

緊緻子集 · qf-mod40-compact-finite-compactness · candidate





## 19. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-finite-compactness；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, relative_open_count, compact, empty_subset, certificate] 欄序回答。

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

Wave6第三層核對=([2, 3, 4], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0019/)

緊緻子集 · qf-mod40-compact-finite-compactness · candidate





## 20. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-finite-compactness；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, relative_open_count, compact, empty_subset, certificate] 欄序回答。

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

Wave6第三層核對=([2, 3, 4], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0020/)

緊緻子集 · qf-mod40-compact-finite-compactness · candidate





## 21. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-finite-compactness；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, relative_open_count, compact, empty_subset, certificate] 欄序回答。

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

Wave6第三層核對=([1, 3, 4], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0021/)

緊緻子集 · qf-mod40-compact-finite-compactness · candidate





## 22. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-finite-compactness；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, relative_open_count, compact, empty_subset, certificate] 欄序回答。

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

Wave6第三層核對=([1, 3, 4], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0022/)

緊緻子集 · qf-mod40-compact-finite-compactness · candidate





## 23. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-finite-compactness；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, relative_open_count, compact, empty_subset, certificate] 欄序回答。

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

Wave6第三層核對=([1, 2, 4], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0023/)

緊緻子集 · qf-mod40-compact-finite-compactness · candidate





## 24. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-finite-compactness；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, relative_open_count, compact, empty_subset, certificate] 欄序回答。

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

Wave6第三層核對=([1, 2, 4], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0024/)

緊緻子集 · qf-mod40-compact-finite-compactness · candidate





## 25. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-finite-compactness；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, relative_open_count, compact, empty_subset, certificate] 欄序回答。

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

Wave6第三層核對=([0, 3, 4], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0025/)

緊緻子集 · qf-mod40-compact-finite-compactness · candidate





## 26. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-open-cover-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],"cover":[[],[1],[1,3],[1,3,4]]}。請依 [cover, covers_subset, union, boundary] 欄序回答。

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

Wave6第三層核對=([[], [1], [1, 3], [1, 3, 4]], 是, [1, 3, 4], single_cover_audit_not_general_compactness_proof)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0026/)

緊緻子集 · qf-mod40-compact-open-cover-audit · candidate





## 27. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-open-cover-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],"cover":[[],[1],[1,3,4],[1,4]]}。請依 [cover, covers_subset, union, boundary] 欄序回答。

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

Wave6第三層核對=([[], [1], [1, 3, 4], [1, 4]], 是, [1, 3, 4], single_cover_audit_not_general_compactness_proof)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0027/)

緊緻子集 · qf-mod40-compact-open-cover-audit · candidate





## 28. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-open-cover-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],"cover":[[],[1],[1,2],[1,2,4]]}。請依 [cover, covers_subset, union, boundary] 欄序回答。

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

Wave6第三層核對=([[], [1], [1, 2], [1, 2, 4]], 是, [1, 2, 4], single_cover_audit_not_general_compactness_proof)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0028/)

緊緻子集 · qf-mod40-compact-open-cover-audit · candidate





## 29. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-open-cover-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],"cover":[[],[1],[1,2,4],[1,4]]}。請依 [cover, covers_subset, union, boundary] 欄序回答。

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

Wave6第三層核對=([[], [1], [1, 2, 4], [1, 4]], 是, [1, 2, 4], single_cover_audit_not_general_compactness_proof)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0029/)

緊緻子集 · qf-mod40-compact-open-cover-audit · candidate





## 30. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-open-cover-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],"cover":[[],[1],[1,2],[1,2,3]]}。請依 [cover, covers_subset, union, boundary] 欄序回答。

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

Wave6第三層核對=([[], [1], [1, 2], [1, 2, 3]], 是, [1, 2, 3], single_cover_audit_not_general_compactness_proof)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0030/)

緊緻子集 · qf-mod40-compact-open-cover-audit · candidate





## 31. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-open-cover-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],"cover":[[],[1],[1,2,3],[1,3]]}。請依 [cover, covers_subset, union, boundary] 欄序回答。

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

Wave6第三層核對=([[], [1], [1, 2, 3], [1, 3]], 是, [1, 2, 3], single_cover_audit_not_general_compactness_proof)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0031/)

緊緻子集 · qf-mod40-compact-open-cover-audit · candidate





## 32. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-open-cover-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],"cover":[[],[2],[2,3],[2,3,4]]}。請依 [cover, covers_subset, union, boundary] 欄序回答。

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

Wave6第三層核對=([[], [2], [2, 3], [2, 3, 4]], 是, [2, 3, 4], single_cover_audit_not_general_compactness_proof)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0032/)

緊緻子集 · qf-mod40-compact-open-cover-audit · candidate





## 33. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-open-cover-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],"cover":[[],[2],[2,3,4],[2,4]]}。請依 [cover, covers_subset, union, boundary] 欄序回答。

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

Wave6第三層核對=([[], [2], [2, 3, 4], [2, 4]], 是, [2, 3, 4], single_cover_audit_not_general_compactness_proof)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0033/)

緊緻子集 · qf-mod40-compact-open-cover-audit · candidate





## 34. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-open-cover-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],"cover":[[],[1,2],[1,2,4],[2]]}。請依 [cover, covers_subset, union, boundary] 欄序回答。

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

Wave6第三層核對=([[], [1, 2], [1, 2, 4], [2]], 是, [1, 2, 4], single_cover_audit_not_general_compactness_proof)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0034/)

緊緻子集 · qf-mod40-compact-open-cover-audit · candidate





## 35. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-open-cover-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],"cover":[[],[1,2,4],[2],[2,4]]}。請依 [cover, covers_subset, union, boundary] 欄序回答。

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

Wave6第三層核對=([[], [1, 2, 4], [2], [2, 4]], 是, [1, 2, 4], single_cover_audit_not_general_compactness_proof)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0035/)

緊緻子集 · qf-mod40-compact-open-cover-audit · candidate





## 36. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-open-cover-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],"cover":[[],[1,2],[1,2,3],[2]]}。請依 [cover, covers_subset, union, boundary] 欄序回答。

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

Wave6第三層核對=([[], [1, 2], [1, 2, 3], [2]], 是, [1, 2, 3], single_cover_audit_not_general_compactness_proof)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0036/)

緊緻子集 · qf-mod40-compact-open-cover-audit · candidate





## 37. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-open-cover-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],"cover":[[],[1,2,3],[2],[2,3]]}。請依 [cover, covers_subset, union, boundary] 欄序回答。

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

Wave6第三層核對=([[], [1, 2, 3], [2], [2, 3]], 是, [1, 2, 3], single_cover_audit_not_general_compactness_proof)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0037/)

緊緻子集 · qf-mod40-compact-open-cover-audit · candidate





## 38. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-open-cover-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],"cover":[[],[2,3],[2,3,4],[3]]}。請依 [cover, covers_subset, union, boundary] 欄序回答。

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

Wave6第三層核對=([[], [2, 3], [2, 3, 4], [3]], 是, [2, 3, 4], single_cover_audit_not_general_compactness_proof)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0038/)

緊緻子集 · qf-mod40-compact-open-cover-audit · candidate





## 39. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-open-cover-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],"cover":[[],[2,3,4],[3],[3,4]]}。請依 [cover, covers_subset, union, boundary] 欄序回答。

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

Wave6第三層核對=([[], [2, 3, 4], [3], [3, 4]], 是, [2, 3, 4], single_cover_audit_not_general_compactness_proof)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0039/)

緊緻子集 · qf-mod40-compact-open-cover-audit · candidate





## 40. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-open-cover-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],"cover":[[],[1,3],[1,3,4],[3]]}。請依 [cover, covers_subset, union, boundary] 欄序回答。

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

Wave6第三層核對=([[], [1, 3], [1, 3, 4], [3]], 是, [1, 3, 4], single_cover_audit_not_general_compactness_proof)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0040/)

緊緻子集 · qf-mod40-compact-open-cover-audit · candidate





## 41. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-open-cover-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],"cover":[[],[1,3,4],[3],[3,4]]}。請依 [cover, covers_subset, union, boundary] 欄序回答。

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

Wave6第三層核對=([[], [1, 3, 4], [3], [3, 4]], 是, [1, 3, 4], single_cover_audit_not_general_compactness_proof)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0041/)

緊緻子集 · qf-mod40-compact-open-cover-audit · candidate





## 42. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-open-cover-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],"cover":[[],[1,2,3],[1,3],[3]]}。請依 [cover, covers_subset, union, boundary] 欄序回答。

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

Wave6第三層核對=([[], [1, 2, 3], [1, 3], [3]], 是, [1, 2, 3], single_cover_audit_not_general_compactness_proof)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0042/)

緊緻子集 · qf-mod40-compact-open-cover-audit · candidate





## 43. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-open-cover-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],"cover":[[],[1,2,3],[2,3],[3]]}。請依 [cover, covers_subset, union, boundary] 欄序回答。

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

Wave6第三層核對=([[], [1, 2, 3], [2, 3], [3]], 是, [1, 2, 3], single_cover_audit_not_general_compactness_proof)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0043/)

緊緻子集 · qf-mod40-compact-open-cover-audit · candidate





## 44. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-open-cover-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],"cover":[[],[2,3,4],[2,4],[4]]}。請依 [cover, covers_subset, union, boundary] 欄序回答。

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

Wave6第三層核對=([[], [2, 3, 4], [2, 4], [4]], 是, [2, 3, 4], single_cover_audit_not_general_compactness_proof)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0044/)

緊緻子集 · qf-mod40-compact-open-cover-audit · candidate





## 45. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-open-cover-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],"cover":[[],[2,3,4],[3,4],[4]]}。請依 [cover, covers_subset, union, boundary] 欄序回答。

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

Wave6第三層核對=([[], [2, 3, 4], [3, 4], [4]], 是, [2, 3, 4], single_cover_audit_not_general_compactness_proof)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0045/)

緊緻子集 · qf-mod40-compact-open-cover-audit · candidate





## 46. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-open-cover-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],"cover":[[],[1,3,4],[1,4],[4]]}。請依 [cover, covers_subset, union, boundary] 欄序回答。

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

Wave6第三層核對=([[], [1, 3, 4], [1, 4], [4]], 是, [1, 3, 4], single_cover_audit_not_general_compactness_proof)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0046/)

緊緻子集 · qf-mod40-compact-open-cover-audit · candidate





## 47. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-open-cover-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],"cover":[[],[1,3,4],[3,4],[4]]}。請依 [cover, covers_subset, union, boundary] 欄序回答。

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

Wave6第三層核對=([[], [1, 3, 4], [3, 4], [4]], 是, [1, 3, 4], single_cover_audit_not_general_compactness_proof)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0047/)

緊緻子集 · qf-mod40-compact-open-cover-audit · candidate





## 48. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-open-cover-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],"cover":[[],[1,2,4],[1,4],[4]]}。請依 [cover, covers_subset, union, boundary] 欄序回答。

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

Wave6第三層核對=([[], [1, 2, 4], [1, 4], [4]], 是, [1, 2, 4], single_cover_audit_not_general_compactness_proof)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0048/)

緊緻子集 · qf-mod40-compact-open-cover-audit · candidate





## 49. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-open-cover-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],"cover":[[],[1,2,4],[2,4],[4]]}。請依 [cover, covers_subset, union, boundary] 欄序回答。

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

Wave6第三層核對=([[], [1, 2, 4], [2, 4], [4]], 是, [1, 2, 4], single_cover_audit_not_general_compactness_proof)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0049/)

緊緻子集 · qf-mod40-compact-open-cover-audit · candidate





## 50. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-open-cover-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],"cover":[[],[0],[0,3],[0,3,4]]}。請依 [cover, covers_subset, union, boundary] 欄序回答。

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

Wave6第三層核對=([[], [0], [0, 3], [0, 3, 4]], 是, [0, 3, 4], single_cover_audit_not_general_compactness_proof)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0050/)

緊緻子集 · qf-mod40-compact-open-cover-audit · candidate





## 51. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-subcover-certificate；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],"cover":[[],[1],[1,3],[1,3,4]],"selected":[3]}。請依 [selected_indices, selected_sets, covers_subset, selected_from_original, certificate] 欄序回答。

covers_subset與selected_from_original分開；選到原cover中的集合不保證已覆蓋K，也不聲稱minimum subcover。

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

Wave6第三層核對=([3], [[1, 3, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0051/)

緊緻子集 · qf-mod40-compact-subcover-certificate · candidate





## 52. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-subcover-certificate；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],"cover":[[],[1],[1,3,4],[1,4]],"selected":[2]}。請依 [selected_indices, selected_sets, covers_subset, selected_from_original, certificate] 欄序回答。

covers_subset與selected_from_original分開；選到原cover中的集合不保證已覆蓋K，也不聲稱minimum subcover。

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

Wave6第三層核對=([2], [[1, 3, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0052/)

緊緻子集 · qf-mod40-compact-subcover-certificate · candidate





## 53. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-subcover-certificate；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],"cover":[[],[1],[1,2],[1,2,4]],"selected":[3]}。請依 [selected_indices, selected_sets, covers_subset, selected_from_original, certificate] 欄序回答。

covers_subset與selected_from_original分開；選到原cover中的集合不保證已覆蓋K，也不聲稱minimum subcover。

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

Wave6第三層核對=([3], [[1, 2, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0053/)

緊緻子集 · qf-mod40-compact-subcover-certificate · candidate





## 54. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-subcover-certificate；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],"cover":[[],[1],[1,2,4],[1,4]],"selected":[2]}。請依 [selected_indices, selected_sets, covers_subset, selected_from_original, certificate] 欄序回答。

covers_subset與selected_from_original分開；選到原cover中的集合不保證已覆蓋K，也不聲稱minimum subcover。

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

Wave6第三層核對=([2], [[1, 2, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0054/)

緊緻子集 · qf-mod40-compact-subcover-certificate · candidate





## 55. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-subcover-certificate；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],"cover":[[],[1],[1,2],[1,2,3]],"selected":[3]}。請依 [selected_indices, selected_sets, covers_subset, selected_from_original, certificate] 欄序回答。

covers_subset與selected_from_original分開；選到原cover中的集合不保證已覆蓋K，也不聲稱minimum subcover。

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

Wave6第三層核對=([3], [[1, 2, 3]], 是, 是, finite_subcover_selected_only_from_original_cover)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0055/)

緊緻子集 · qf-mod40-compact-subcover-certificate · candidate





## 56. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-subcover-certificate；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],"cover":[[],[1],[1,2,3],[1,3]],"selected":[2]}。請依 [selected_indices, selected_sets, covers_subset, selected_from_original, certificate] 欄序回答。

covers_subset與selected_from_original分開；選到原cover中的集合不保證已覆蓋K，也不聲稱minimum subcover。

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

Wave6第三層核對=([2], [[1, 2, 3]], 是, 是, finite_subcover_selected_only_from_original_cover)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0056/)

緊緻子集 · qf-mod40-compact-subcover-certificate · candidate





## 57. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-subcover-certificate；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],"cover":[[],[2],[2,3],[2,3,4]],"selected":[3]}。請依 [selected_indices, selected_sets, covers_subset, selected_from_original, certificate] 欄序回答。

covers_subset與selected_from_original分開；選到原cover中的集合不保證已覆蓋K，也不聲稱minimum subcover。

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

Wave6第三層核對=([3], [[2, 3, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0057/)

緊緻子集 · qf-mod40-compact-subcover-certificate · candidate





## 58. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-subcover-certificate；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],"cover":[[],[2],[2,3,4],[2,4]],"selected":[2]}。請依 [selected_indices, selected_sets, covers_subset, selected_from_original, certificate] 欄序回答。

covers_subset與selected_from_original分開；選到原cover中的集合不保證已覆蓋K，也不聲稱minimum subcover。

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

Wave6第三層核對=([2], [[2, 3, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0058/)

緊緻子集 · qf-mod40-compact-subcover-certificate · candidate





## 59. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-subcover-certificate；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],"cover":[[],[1,2],[1,2,4],[2]],"selected":[2]}。請依 [selected_indices, selected_sets, covers_subset, selected_from_original, certificate] 欄序回答。

covers_subset與selected_from_original分開；選到原cover中的集合不保證已覆蓋K，也不聲稱minimum subcover。

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

Wave6第三層核對=([2], [[1, 2, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0059/)

緊緻子集 · qf-mod40-compact-subcover-certificate · candidate





## 60. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-subcover-certificate；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],"cover":[[],[1,2,4],[2],[2,4]],"selected":[1]}。請依 [selected_indices, selected_sets, covers_subset, selected_from_original, certificate] 欄序回答。

covers_subset與selected_from_original分開；選到原cover中的集合不保證已覆蓋K，也不聲稱minimum subcover。

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

Wave6第三層核對=([1], [[1, 2, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0060/)

緊緻子集 · qf-mod40-compact-subcover-certificate · candidate





## 61. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-subcover-certificate；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],"cover":[[],[1,2],[1,2,3],[2]],"selected":[2]}。請依 [selected_indices, selected_sets, covers_subset, selected_from_original, certificate] 欄序回答。

covers_subset與selected_from_original分開；選到原cover中的集合不保證已覆蓋K，也不聲稱minimum subcover。

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

Wave6第三層核對=([2], [[1, 2, 3]], 是, 是, finite_subcover_selected_only_from_original_cover)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0061/)

緊緻子集 · qf-mod40-compact-subcover-certificate · candidate





## 62. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-subcover-certificate；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],"cover":[[],[1,2,3],[2],[2,3]],"selected":[1]}。請依 [selected_indices, selected_sets, covers_subset, selected_from_original, certificate] 欄序回答。

covers_subset與selected_from_original分開；選到原cover中的集合不保證已覆蓋K，也不聲稱minimum subcover。

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

Wave6第三層核對=([1], [[1, 2, 3]], 是, 是, finite_subcover_selected_only_from_original_cover)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0062/)

緊緻子集 · qf-mod40-compact-subcover-certificate · candidate





## 63. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-subcover-certificate；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],"cover":[[],[2,3],[2,3,4],[3]],"selected":[2]}。請依 [selected_indices, selected_sets, covers_subset, selected_from_original, certificate] 欄序回答。

covers_subset與selected_from_original分開；選到原cover中的集合不保證已覆蓋K，也不聲稱minimum subcover。

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

Wave6第三層核對=([2], [[2, 3, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0063/)

緊緻子集 · qf-mod40-compact-subcover-certificate · candidate





## 64. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-subcover-certificate；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],"cover":[[],[2,3,4],[3],[3,4]],"selected":[1]}。請依 [selected_indices, selected_sets, covers_subset, selected_from_original, certificate] 欄序回答。

covers_subset與selected_from_original分開；選到原cover中的集合不保證已覆蓋K，也不聲稱minimum subcover。

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

Wave6第三層核對=([1], [[2, 3, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0064/)

緊緻子集 · qf-mod40-compact-subcover-certificate · candidate





## 65. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-subcover-certificate；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],"cover":[[],[1,3],[1,3,4],[3]],"selected":[2]}。請依 [selected_indices, selected_sets, covers_subset, selected_from_original, certificate] 欄序回答。

covers_subset與selected_from_original分開；選到原cover中的集合不保證已覆蓋K，也不聲稱minimum subcover。

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

Wave6第三層核對=([2], [[1, 3, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0065/)

緊緻子集 · qf-mod40-compact-subcover-certificate · candidate





## 66. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-subcover-certificate；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],"cover":[[],[1,3,4],[3],[3,4]],"selected":[1]}。請依 [selected_indices, selected_sets, covers_subset, selected_from_original, certificate] 欄序回答。

covers_subset與selected_from_original分開；選到原cover中的集合不保證已覆蓋K，也不聲稱minimum subcover。

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

Wave6第三層核對=([1], [[1, 3, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0066/)

緊緻子集 · qf-mod40-compact-subcover-certificate · candidate





## 67. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-subcover-certificate；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],"cover":[[],[1,2,3],[1,3],[3]],"selected":[1]}。請依 [selected_indices, selected_sets, covers_subset, selected_from_original, certificate] 欄序回答。

covers_subset與selected_from_original分開；選到原cover中的集合不保證已覆蓋K，也不聲稱minimum subcover。

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

Wave6第三層核對=([1], [[1, 2, 3]], 是, 是, finite_subcover_selected_only_from_original_cover)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0067/)

緊緻子集 · qf-mod40-compact-subcover-certificate · candidate





## 68. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-subcover-certificate；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],"cover":[[],[1,2,3],[2,3],[3]],"selected":[1]}。請依 [selected_indices, selected_sets, covers_subset, selected_from_original, certificate] 欄序回答。

covers_subset與selected_from_original分開；選到原cover中的集合不保證已覆蓋K，也不聲稱minimum subcover。

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

Wave6第三層核對=([1], [[1, 2, 3]], 是, 是, finite_subcover_selected_only_from_original_cover)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0068/)

緊緻子集 · qf-mod40-compact-subcover-certificate · candidate





## 69. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-subcover-certificate；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],"cover":[[],[2,3,4],[2,4],[4]],"selected":[1]}。請依 [selected_indices, selected_sets, covers_subset, selected_from_original, certificate] 欄序回答。

covers_subset與selected_from_original分開；選到原cover中的集合不保證已覆蓋K，也不聲稱minimum subcover。

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

Wave6第三層核對=([1], [[2, 3, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0069/)

緊緻子集 · qf-mod40-compact-subcover-certificate · candidate





## 70. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-subcover-certificate；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],"cover":[[],[2,3,4],[3,4],[4]],"selected":[1]}。請依 [selected_indices, selected_sets, covers_subset, selected_from_original, certificate] 欄序回答。

covers_subset與selected_from_original分開；選到原cover中的集合不保證已覆蓋K，也不聲稱minimum subcover。

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

Wave6第三層核對=([1], [[2, 3, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0070/)

緊緻子集 · qf-mod40-compact-subcover-certificate · candidate





## 71. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-subcover-certificate；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],"cover":[[],[1,3,4],[1,4],[4]],"selected":[1]}。請依 [selected_indices, selected_sets, covers_subset, selected_from_original, certificate] 欄序回答。

covers_subset與selected_from_original分開；選到原cover中的集合不保證已覆蓋K，也不聲稱minimum subcover。

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

Wave6第三層核對=([1], [[1, 3, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0071/)

緊緻子集 · qf-mod40-compact-subcover-certificate · candidate





## 72. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-subcover-certificate；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],"cover":[[],[1,3,4],[3,4],[4]],"selected":[1]}。請依 [selected_indices, selected_sets, covers_subset, selected_from_original, certificate] 欄序回答。

covers_subset與selected_from_original分開；選到原cover中的集合不保證已覆蓋K，也不聲稱minimum subcover。

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

Wave6第三層核對=([1], [[1, 3, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0072/)

緊緻子集 · qf-mod40-compact-subcover-certificate · candidate





## 73. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-subcover-certificate；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],"cover":[[],[1,2,4],[1,4],[4]],"selected":[1]}。請依 [selected_indices, selected_sets, covers_subset, selected_from_original, certificate] 欄序回答。

covers_subset與selected_from_original分開；選到原cover中的集合不保證已覆蓋K，也不聲稱minimum subcover。

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

Wave6第三層核對=([1], [[1, 2, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0073/)

緊緻子集 · qf-mod40-compact-subcover-certificate · candidate





## 74. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-subcover-certificate；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],"cover":[[],[1,2,4],[2,4],[4]],"selected":[1]}。請依 [selected_indices, selected_sets, covers_subset, selected_from_original, certificate] 欄序回答。

covers_subset與selected_from_original分開；選到原cover中的集合不保證已覆蓋K，也不聲稱minimum subcover。

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

Wave6第三層核對=([1], [[1, 2, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0074/)

緊緻子集 · qf-mod40-compact-subcover-certificate · candidate





## 75. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-subcover-certificate；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],"cover":[[],[0],[0,3],[0,3,4]],"selected":[3]}。請依 [selected_indices, selected_sets, covers_subset, selected_from_original, certificate] 欄序回答。

covers_subset與selected_from_original分開；選到原cover中的集合不保證已覆蓋K，也不聲稱minimum subcover。

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

Wave6第三層核對=([3], [[0, 3, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0075/)

緊緻子集 · qf-mod40-compact-subcover-certificate · candidate





## 76. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-nonproperty-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]}。請依 [subset, compact, general_ambient_closedness_claim, general_boundedness_claim, boundary] 欄序回答。

後兩個否是不作一般母空間closedness／boundedness推論，不是逐一判定此K不closed或不bounded；一般拓撲沒有預設metric。

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

Wave6第三層核對=([1, 3, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0076/)

緊緻子集 · qf-mod40-compact-nonproperty-boundary · candidate





## 77. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-nonproperty-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]}。請依 [subset, compact, general_ambient_closedness_claim, general_boundedness_claim, boundary] 欄序回答。

後兩個否是不作一般母空間closedness／boundedness推論，不是逐一判定此K不closed或不bounded；一般拓撲沒有預設metric。

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

Wave6第三層核對=([1, 3, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0077/)

緊緻子集 · qf-mod40-compact-nonproperty-boundary · candidate





## 78. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-nonproperty-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]}。請依 [subset, compact, general_ambient_closedness_claim, general_boundedness_claim, boundary] 欄序回答。

後兩個否是不作一般母空間closedness／boundedness推論，不是逐一判定此K不closed或不bounded；一般拓撲沒有預設metric。

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

Wave6第三層核對=([1, 2, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0078/)

緊緻子集 · qf-mod40-compact-nonproperty-boundary · candidate





## 79. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-nonproperty-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]}。請依 [subset, compact, general_ambient_closedness_claim, general_boundedness_claim, boundary] 欄序回答。

後兩個否是不作一般母空間closedness／boundedness推論，不是逐一判定此K不closed或不bounded；一般拓撲沒有預設metric。

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

Wave6第三層核對=([1, 2, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0079/)

緊緻子集 · qf-mod40-compact-nonproperty-boundary · candidate





## 80. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-nonproperty-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]}。請依 [subset, compact, general_ambient_closedness_claim, general_boundedness_claim, boundary] 欄序回答。

後兩個否是不作一般母空間closedness／boundedness推論，不是逐一判定此K不closed或不bounded；一般拓撲沒有預設metric。

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

Wave6第三層核對=([1, 2, 3], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0080/)

緊緻子集 · qf-mod40-compact-nonproperty-boundary · candidate





## 81. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-nonproperty-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]}。請依 [subset, compact, general_ambient_closedness_claim, general_boundedness_claim, boundary] 欄序回答。

後兩個否是不作一般母空間closedness／boundedness推論，不是逐一判定此K不closed或不bounded；一般拓撲沒有預設metric。

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

Wave6第三層核對=([1, 2, 3], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0081/)

緊緻子集 · qf-mod40-compact-nonproperty-boundary · candidate





## 82. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-nonproperty-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]}。請依 [subset, compact, general_ambient_closedness_claim, general_boundedness_claim, boundary] 欄序回答。

後兩個否是不作一般母空間closedness／boundedness推論，不是逐一判定此K不closed或不bounded；一般拓撲沒有預設metric。

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

Wave6第三層核對=([2, 3, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0082/)

緊緻子集 · qf-mod40-compact-nonproperty-boundary · candidate





## 83. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-nonproperty-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]}。請依 [subset, compact, general_ambient_closedness_claim, general_boundedness_claim, boundary] 欄序回答。

後兩個否是不作一般母空間closedness／boundedness推論，不是逐一判定此K不closed或不bounded；一般拓撲沒有預設metric。

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

Wave6第三層核對=([2, 3, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0083/)

緊緻子集 · qf-mod40-compact-nonproperty-boundary · candidate





## 84. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-nonproperty-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]}。請依 [subset, compact, general_ambient_closedness_claim, general_boundedness_claim, boundary] 欄序回答。

後兩個否是不作一般母空間closedness／boundedness推論，不是逐一判定此K不closed或不bounded；一般拓撲沒有預設metric。

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

Wave6第三層核對=([1, 2, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0084/)

緊緻子集 · qf-mod40-compact-nonproperty-boundary · candidate





## 85. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-nonproperty-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]}。請依 [subset, compact, general_ambient_closedness_claim, general_boundedness_claim, boundary] 欄序回答。

後兩個否是不作一般母空間closedness／boundedness推論，不是逐一判定此K不closed或不bounded；一般拓撲沒有預設metric。

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

Wave6第三層核對=([1, 2, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0085/)

緊緻子集 · qf-mod40-compact-nonproperty-boundary · candidate





## 86. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-nonproperty-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]}。請依 [subset, compact, general_ambient_closedness_claim, general_boundedness_claim, boundary] 欄序回答。

後兩個否是不作一般母空間closedness／boundedness推論，不是逐一判定此K不closed或不bounded；一般拓撲沒有預設metric。

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

Wave6第三層核對=([1, 2, 3], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0086/)

緊緻子集 · qf-mod40-compact-nonproperty-boundary · candidate





## 87. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-nonproperty-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]}。請依 [subset, compact, general_ambient_closedness_claim, general_boundedness_claim, boundary] 欄序回答。

後兩個否是不作一般母空間closedness／boundedness推論，不是逐一判定此K不closed或不bounded；一般拓撲沒有預設metric。

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

Wave6第三層核對=([1, 2, 3], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0087/)

緊緻子集 · qf-mod40-compact-nonproperty-boundary · candidate





## 88. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-nonproperty-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]}。請依 [subset, compact, general_ambient_closedness_claim, general_boundedness_claim, boundary] 欄序回答。

後兩個否是不作一般母空間closedness／boundedness推論，不是逐一判定此K不closed或不bounded；一般拓撲沒有預設metric。

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

Wave6第三層核對=([2, 3, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0088/)

緊緻子集 · qf-mod40-compact-nonproperty-boundary · candidate





## 89. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-nonproperty-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]}。請依 [subset, compact, general_ambient_closedness_claim, general_boundedness_claim, boundary] 欄序回答。

後兩個否是不作一般母空間closedness／boundedness推論，不是逐一判定此K不closed或不bounded；一般拓撲沒有預設metric。

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

Wave6第三層核對=([2, 3, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0089/)

緊緻子集 · qf-mod40-compact-nonproperty-boundary · candidate





## 90. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-nonproperty-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]}。請依 [subset, compact, general_ambient_closedness_claim, general_boundedness_claim, boundary] 欄序回答。

後兩個否是不作一般母空間closedness／boundedness推論，不是逐一判定此K不closed或不bounded；一般拓撲沒有預設metric。

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

Wave6第三層核對=([1, 3, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0090/)

緊緻子集 · qf-mod40-compact-nonproperty-boundary · candidate





## 91. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-nonproperty-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]}。請依 [subset, compact, general_ambient_closedness_claim, general_boundedness_claim, boundary] 欄序回答。

後兩個否是不作一般母空間closedness／boundedness推論，不是逐一判定此K不closed或不bounded；一般拓撲沒有預設metric。

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

Wave6第三層核對=([1, 3, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0091/)

緊緻子集 · qf-mod40-compact-nonproperty-boundary · candidate





## 92. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-nonproperty-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]}。請依 [subset, compact, general_ambient_closedness_claim, general_boundedness_claim, boundary] 欄序回答。

後兩個否是不作一般母空間closedness／boundedness推論，不是逐一判定此K不closed或不bounded；一般拓撲沒有預設metric。

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

Wave6第三層核對=([1, 2, 3], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0092/)

緊緻子集 · qf-mod40-compact-nonproperty-boundary · candidate





## 93. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-nonproperty-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]}。請依 [subset, compact, general_ambient_closedness_claim, general_boundedness_claim, boundary] 欄序回答。

後兩個否是不作一般母空間closedness／boundedness推論，不是逐一判定此K不closed或不bounded；一般拓撲沒有預設metric。

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

Wave6第三層核對=([1, 2, 3], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0093/)

緊緻子集 · qf-mod40-compact-nonproperty-boundary · candidate





## 94. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-nonproperty-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]}。請依 [subset, compact, general_ambient_closedness_claim, general_boundedness_claim, boundary] 欄序回答。

後兩個否是不作一般母空間closedness／boundedness推論，不是逐一判定此K不closed或不bounded；一般拓撲沒有預設metric。

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

Wave6第三層核對=([2, 3, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0094/)

緊緻子集 · qf-mod40-compact-nonproperty-boundary · candidate





## 95. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-nonproperty-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]}。請依 [subset, compact, general_ambient_closedness_claim, general_boundedness_claim, boundary] 欄序回答。

後兩個否是不作一般母空間closedness／boundedness推論，不是逐一判定此K不closed或不bounded；一般拓撲沒有預設metric。

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

Wave6第三層核對=([2, 3, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0095/)

緊緻子集 · qf-mod40-compact-nonproperty-boundary · candidate





## 96. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-nonproperty-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]}。請依 [subset, compact, general_ambient_closedness_claim, general_boundedness_claim, boundary] 欄序回答。

後兩個否是不作一般母空間closedness／boundedness推論，不是逐一判定此K不closed或不bounded；一般拓撲沒有預設metric。

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

Wave6第三層核對=([1, 3, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0096/)

緊緻子集 · qf-mod40-compact-nonproperty-boundary · candidate





## 97. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-nonproperty-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]}。請依 [subset, compact, general_ambient_closedness_claim, general_boundedness_claim, boundary] 欄序回答。

後兩個否是不作一般母空間closedness／boundedness推論，不是逐一判定此K不closed或不bounded；一般拓撲沒有預設metric。

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

Wave6第三層核對=([1, 3, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0097/)

緊緻子集 · qf-mod40-compact-nonproperty-boundary · candidate





## 98. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-nonproperty-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]}。請依 [subset, compact, general_ambient_closedness_claim, general_boundedness_claim, boundary] 欄序回答。

後兩個否是不作一般母空間closedness／boundedness推論，不是逐一判定此K不closed或不bounded；一般拓撲沒有預設metric。

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

Wave6第三層核對=([1, 2, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0098/)

緊緻子集 · qf-mod40-compact-nonproperty-boundary · candidate





## 99. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-nonproperty-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]}。請依 [subset, compact, general_ambient_closedness_claim, general_boundedness_claim, boundary] 欄序回答。

後兩個否是不作一般母空間closedness／boundedness推論，不是逐一判定此K不closed或不bounded；一般拓撲沒有預設metric。

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

Wave6第三層核對=([1, 2, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0099/)

緊緻子集 · qf-mod40-compact-nonproperty-boundary · candidate





## 100. 緊緻子集

完整有限subspace topology與relative open covers。操作=compact-nonproperty-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]}。請依 [subset, compact, general_ambient_closedness_claim, general_boundedness_claim, boundary] 欄序回答。

後兩個否是不作一般母空間closedness／boundedness推論，不是逐一判定此K不closed或不bounded；一般拓撲沒有預設metric。

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

Wave6第三層核對=([0, 3, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r03-compact-subset-0100/)

緊緻子集 · qf-mod40-compact-nonproperty-boundary · candidate



[原始題目 JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261014-advance-20261109-r03-compact-subset-foundations/questions.jsonl) · [驗收報告](https://ocme.evemisslab.com/data/questions/batches/batch-20261014-advance-20261109-r03-compact-subset-foundations/validation-report.json)