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
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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。
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([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）
緊緻子集 · qf-mod40-compact-nonproperty-boundary · candidate
原始題目 JSONL · 驗收報告