# 緊緻集的連續像基礎 · 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-20261110-r03-continuous-image-of-compact-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. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-image-set；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[0,0,0],"subset":[0,1,2]}。請依 [subset, map, image, finite_compactness_certificate, certificate] 欄序回答。

此步只算有限K的精確像及有限性compact證書；continuity由另一審核步驟判斷，不以有限像compact反推一般domain compact。

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

Wave6第四層核對=([0, 1, 2], [0, 0, 0], [0], 是, finite_compact_source_subset_exact_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0001/)

緊緻集的連續像 · qf-mod41-compactimg-image-set · candidate





## 2. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-image-set；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[1,0,0],"subset":[0,1,2]}。請依 [subset, map, image, finite_compactness_certificate, certificate] 欄序回答。

此步只算有限K的精確像及有限性compact證書；continuity由另一審核步驟判斷，不以有限像compact反推一般domain compact。

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

Wave6第四層核對=([0, 1, 2], [1, 0, 0], [0, 1], 是, finite_compact_source_subset_exact_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0002/)

緊緻集的連續像 · qf-mod41-compactimg-image-set · candidate





## 3. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-image-set；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[2,0,0],"subset":[0,1,2]}。請依 [subset, map, image, finite_compactness_certificate, certificate] 欄序回答。

此步只算有限K的精確像及有限性compact證書；continuity由另一審核步驟判斷，不以有限像compact反推一般domain compact。

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

Wave6第四層核對=([0, 1, 2], [2, 0, 0], [0, 2], 是, finite_compact_source_subset_exact_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0003/)

緊緻集的連續像 · qf-mod41-compactimg-image-set · candidate





## 4. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-image-set；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[0,1,0],"subset":[0,1,2]}。請依 [subset, map, image, finite_compactness_certificate, certificate] 欄序回答。

此步只算有限K的精確像及有限性compact證書；continuity由另一審核步驟判斷，不以有限像compact反推一般domain compact。

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

Wave6第四層核對=([0, 1, 2], [0, 1, 0], [0, 1], 是, finite_compact_source_subset_exact_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0004/)

緊緻集的連續像 · qf-mod41-compactimg-image-set · candidate





## 5. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-image-set；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[1,1,0],"subset":[0,1,2]}。請依 [subset, map, image, finite_compactness_certificate, certificate] 欄序回答。

此步只算有限K的精確像及有限性compact證書；continuity由另一審核步驟判斷，不以有限像compact反推一般domain compact。

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

Wave6第四層核對=([0, 1, 2], [1, 1, 0], [0, 1], 是, finite_compact_source_subset_exact_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0005/)

緊緻集的連續像 · qf-mod41-compactimg-image-set · candidate





## 6. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-image-set；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[2,1,0],"subset":[0,1,2]}。請依 [subset, map, image, finite_compactness_certificate, certificate] 欄序回答。

此步只算有限K的精確像及有限性compact證書；continuity由另一審核步驟判斷，不以有限像compact反推一般domain compact。

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

Wave6第四層核對=([0, 1, 2], [2, 1, 0], [0, 1, 2], 是, finite_compact_source_subset_exact_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0006/)

緊緻集的連續像 · qf-mod41-compactimg-image-set · candidate





## 7. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-image-set；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[0,2,0],"subset":[0,1,2]}。請依 [subset, map, image, finite_compactness_certificate, certificate] 欄序回答。

此步只算有限K的精確像及有限性compact證書；continuity由另一審核步驟判斷，不以有限像compact反推一般domain compact。

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

Wave6第四層核對=([0, 1, 2], [0, 2, 0], [0, 2], 是, finite_compact_source_subset_exact_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0007/)

緊緻集的連續像 · qf-mod41-compactimg-image-set · candidate





## 8. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-image-set；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[1,2,0],"subset":[0,1,2]}。請依 [subset, map, image, finite_compactness_certificate, certificate] 欄序回答。

此步只算有限K的精確像及有限性compact證書；continuity由另一審核步驟判斷，不以有限像compact反推一般domain compact。

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

Wave6第四層核對=([0, 1, 2], [1, 2, 0], [0, 1, 2], 是, finite_compact_source_subset_exact_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0008/)

緊緻集的連續像 · qf-mod41-compactimg-image-set · candidate





## 9. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-image-set；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[2,2,0],"subset":[0,1,2]}。請依 [subset, map, image, finite_compactness_certificate, certificate] 欄序回答。

此步只算有限K的精確像及有限性compact證書；continuity由另一審核步驟判斷，不以有限像compact反推一般domain compact。

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

Wave6第四層核對=([0, 1, 2], [2, 2, 0], [0, 2], 是, finite_compact_source_subset_exact_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0009/)

緊緻集的連續像 · qf-mod41-compactimg-image-set · candidate





## 10. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-image-set；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[0,0,1],"subset":[0,1,2]}。請依 [subset, map, image, finite_compactness_certificate, certificate] 欄序回答。

此步只算有限K的精確像及有限性compact證書；continuity由另一審核步驟判斷，不以有限像compact反推一般domain compact。

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

Wave6第四層核對=([0, 1, 2], [0, 0, 1], [0, 1], 是, finite_compact_source_subset_exact_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0010/)

緊緻集的連續像 · qf-mod41-compactimg-image-set · candidate





## 11. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-image-set；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[1,0,1],"subset":[0,1,2]}。請依 [subset, map, image, finite_compactness_certificate, certificate] 欄序回答。

此步只算有限K的精確像及有限性compact證書；continuity由另一審核步驟判斷，不以有限像compact反推一般domain compact。

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

Wave6第四層核對=([0, 1, 2], [1, 0, 1], [0, 1], 是, finite_compact_source_subset_exact_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0011/)

緊緻集的連續像 · qf-mod41-compactimg-image-set · candidate





## 12. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-image-set；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[2,0,1],"subset":[0,1,2]}。請依 [subset, map, image, finite_compactness_certificate, certificate] 欄序回答。

此步只算有限K的精確像及有限性compact證書；continuity由另一審核步驟判斷，不以有限像compact反推一般domain compact。

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

Wave6第四層核對=([0, 1, 2], [2, 0, 1], [0, 1, 2], 是, finite_compact_source_subset_exact_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0012/)

緊緻集的連續像 · qf-mod41-compactimg-image-set · candidate





## 13. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-image-set；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[0,1,1],"subset":[0,1,2]}。請依 [subset, map, image, finite_compactness_certificate, certificate] 欄序回答。

此步只算有限K的精確像及有限性compact證書；continuity由另一審核步驟判斷，不以有限像compact反推一般domain compact。

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

Wave6第四層核對=([0, 1, 2], [0, 1, 1], [0, 1], 是, finite_compact_source_subset_exact_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0013/)

緊緻集的連續像 · qf-mod41-compactimg-image-set · candidate





## 14. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-image-set；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[1,1,1],"subset":[0,1,2]}。請依 [subset, map, image, finite_compactness_certificate, certificate] 欄序回答。

此步只算有限K的精確像及有限性compact證書；continuity由另一審核步驟判斷，不以有限像compact反推一般domain compact。

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

Wave6第四層核對=([0, 1, 2], [1, 1, 1], [1], 是, finite_compact_source_subset_exact_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0014/)

緊緻集的連續像 · qf-mod41-compactimg-image-set · candidate





## 15. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-image-set；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[2,1,1],"subset":[0,1,2]}。請依 [subset, map, image, finite_compactness_certificate, certificate] 欄序回答。

此步只算有限K的精確像及有限性compact證書；continuity由另一審核步驟判斷，不以有限像compact反推一般domain compact。

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

Wave6第四層核對=([0, 1, 2], [2, 1, 1], [1, 2], 是, finite_compact_source_subset_exact_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0015/)

緊緻集的連續像 · qf-mod41-compactimg-image-set · candidate





## 16. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-image-set；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[0,2,1],"subset":[0,1,2]}。請依 [subset, map, image, finite_compactness_certificate, certificate] 欄序回答。

此步只算有限K的精確像及有限性compact證書；continuity由另一審核步驟判斷，不以有限像compact反推一般domain compact。

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

Wave6第四層核對=([0, 1, 2], [0, 2, 1], [0, 1, 2], 是, finite_compact_source_subset_exact_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0016/)

緊緻集的連續像 · qf-mod41-compactimg-image-set · candidate





## 17. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-image-set；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[1,2,1],"subset":[0,1,2]}。請依 [subset, map, image, finite_compactness_certificate, certificate] 欄序回答。

此步只算有限K的精確像及有限性compact證書；continuity由另一審核步驟判斷，不以有限像compact反推一般domain compact。

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

Wave6第四層核對=([0, 1, 2], [1, 2, 1], [1, 2], 是, finite_compact_source_subset_exact_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0017/)

緊緻集的連續像 · qf-mod41-compactimg-image-set · candidate





## 18. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-image-set；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[2,2,1],"subset":[0,1,2]}。請依 [subset, map, image, finite_compactness_certificate, certificate] 欄序回答。

此步只算有限K的精確像及有限性compact證書；continuity由另一審核步驟判斷，不以有限像compact反推一般domain compact。

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

Wave6第四層核對=([0, 1, 2], [2, 2, 1], [1, 2], 是, finite_compact_source_subset_exact_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0018/)

緊緻集的連續像 · qf-mod41-compactimg-image-set · candidate





## 19. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-image-set；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[0,0,2],"subset":[0,1,2]}。請依 [subset, map, image, finite_compactness_certificate, certificate] 欄序回答。

此步只算有限K的精確像及有限性compact證書；continuity由另一審核步驟判斷，不以有限像compact反推一般domain compact。

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

Wave6第四層核對=([0, 1, 2], [0, 0, 2], [0, 2], 是, finite_compact_source_subset_exact_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0019/)

緊緻集的連續像 · qf-mod41-compactimg-image-set · candidate





## 20. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-image-set；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[1,0,2],"subset":[0,1,2]}。請依 [subset, map, image, finite_compactness_certificate, certificate] 欄序回答。

此步只算有限K的精確像及有限性compact證書；continuity由另一審核步驟判斷，不以有限像compact反推一般domain compact。

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

Wave6第四層核對=([0, 1, 2], [1, 0, 2], [0, 1, 2], 是, finite_compact_source_subset_exact_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0020/)

緊緻集的連續像 · qf-mod41-compactimg-image-set · candidate





## 21. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-image-set；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[2,0,2],"subset":[0,1,2]}。請依 [subset, map, image, finite_compactness_certificate, certificate] 欄序回答。

此步只算有限K的精確像及有限性compact證書；continuity由另一審核步驟判斷，不以有限像compact反推一般domain compact。

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

Wave6第四層核對=([0, 1, 2], [2, 0, 2], [0, 2], 是, finite_compact_source_subset_exact_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0021/)

緊緻集的連續像 · qf-mod41-compactimg-image-set · candidate





## 22. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-image-set；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[0,1,2],"subset":[0,1,2]}。請依 [subset, map, image, finite_compactness_certificate, certificate] 欄序回答。

此步只算有限K的精確像及有限性compact證書；continuity由另一審核步驟判斷，不以有限像compact反推一般domain compact。

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

Wave6第四層核對=([0, 1, 2], [0, 1, 2], [0, 1, 2], 是, finite_compact_source_subset_exact_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0022/)

緊緻集的連續像 · qf-mod41-compactimg-image-set · candidate





## 23. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-image-set；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[1,1,2],"subset":[0,1,2]}。請依 [subset, map, image, finite_compactness_certificate, certificate] 欄序回答。

此步只算有限K的精確像及有限性compact證書；continuity由另一審核步驟判斷，不以有限像compact反推一般domain compact。

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

Wave6第四層核對=([0, 1, 2], [1, 1, 2], [1, 2], 是, finite_compact_source_subset_exact_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0023/)

緊緻集的連續像 · qf-mod41-compactimg-image-set · candidate





## 24. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-image-set；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[2,1,2],"subset":[0,1,2]}。請依 [subset, map, image, finite_compactness_certificate, certificate] 欄序回答。

此步只算有限K的精確像及有限性compact證書；continuity由另一審核步驟判斷，不以有限像compact反推一般domain compact。

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

Wave6第四層核對=([0, 1, 2], [2, 1, 2], [1, 2], 是, finite_compact_source_subset_exact_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0024/)

緊緻集的連續像 · qf-mod41-compactimg-image-set · candidate





## 25. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-image-set；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[0,2,2],"subset":[0,1,2]}。請依 [subset, map, image, finite_compactness_certificate, certificate] 欄序回答。

此步只算有限K的精確像及有限性compact證書；continuity由另一審核步驟判斷，不以有限像compact反推一般domain compact。

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

Wave6第四層核對=([0, 1, 2], [0, 2, 2], [0, 2], 是, finite_compact_source_subset_exact_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0025/)

緊緻集的連續像 · qf-mod41-compactimg-image-set · candidate





## 26. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-continuity-audit；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[0,0,0],"subset":[0,1,2]}。請依 [open_preimage_rows, continuous, certificate] 欄序回答。

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

Wave6第四層核對=([[[], []], [[0], [0, 1, 2]], [[0, 1], [0, 1, 2]], [[0, 1, 2], [0, 1, 2]], [[0, 2], [0, 1, 2]], [[1], []], [[1, 2], []], [[2], []]], 是, every_target_open_has_source_open_preimage)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0026/)

緊緻集的連續像 · qf-mod41-compactimg-continuity-audit · candidate





## 27. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-continuity-audit；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[1,0,0],"subset":[0,1,2]}。請依 [open_preimage_rows, continuous, certificate] 欄序回答。

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

Wave6第四層核對=([[[], []], [[0], [1, 2]], [[0, 1], [0, 1, 2]], [[0, 1, 2], [0, 1, 2]], [[0, 2], [1, 2]], [[1], [0]], [[1, 2], [0]], [[2], []]], 是, every_target_open_has_source_open_preimage)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0027/)

緊緻集的連續像 · qf-mod41-compactimg-continuity-audit · candidate





## 28. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-continuity-audit；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[2,0,0],"subset":[0,1,2]}。請依 [open_preimage_rows, continuous, certificate] 欄序回答。

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

Wave6第四層核對=([[[], []], [[0], [1, 2]], [[0, 1], [1, 2]], [[0, 1, 2], [0, 1, 2]], [[0, 2], [0, 1, 2]], [[1], []], [[1, 2], [0]], [[2], [0]]], 是, every_target_open_has_source_open_preimage)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0028/)

緊緻集的連續像 · qf-mod41-compactimg-continuity-audit · candidate





## 29. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-continuity-audit；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[0,1,0],"subset":[0,1,2]}。請依 [open_preimage_rows, continuous, certificate] 欄序回答。

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

Wave6第四層核對=([[[], []], [[0], [0, 2]], [[0, 1], [0, 1, 2]], [[0, 1, 2], [0, 1, 2]], [[0, 2], [0, 2]], [[1], [1]], [[1, 2], [1]], [[2], []]], 是, every_target_open_has_source_open_preimage)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0029/)

緊緻集的連續像 · qf-mod41-compactimg-continuity-audit · candidate





## 30. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-continuity-audit；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[1,1,0],"subset":[0,1,2]}。請依 [open_preimage_rows, continuous, certificate] 欄序回答。

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

Wave6第四層核對=([[[], []], [[0], [2]], [[0, 1], [0, 1, 2]], [[0, 1, 2], [0, 1, 2]], [[0, 2], [2]], [[1], [0, 1]], [[1, 2], [0, 1]], [[2], []]], 是, every_target_open_has_source_open_preimage)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0030/)

緊緻集的連續像 · qf-mod41-compactimg-continuity-audit · candidate





## 31. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-continuity-audit；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[2,1,0],"subset":[0,1,2]}。請依 [open_preimage_rows, continuous, certificate] 欄序回答。

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

Wave6第四層核對=([[[], []], [[0], [2]], [[0, 1], [1, 2]], [[0, 1, 2], [0, 1, 2]], [[0, 2], [0, 2]], [[1], [1]], [[1, 2], [0, 1]], [[2], [0]]], 是, every_target_open_has_source_open_preimage)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0031/)

緊緻集的連續像 · qf-mod41-compactimg-continuity-audit · candidate





## 32. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-continuity-audit；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[0,2,0],"subset":[0,1,2]}。請依 [open_preimage_rows, continuous, certificate] 欄序回答。

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

Wave6第四層核對=([[[], []], [[0], [0, 2]], [[0, 1], [0, 2]], [[0, 1, 2], [0, 1, 2]], [[0, 2], [0, 1, 2]], [[1], []], [[1, 2], [1]], [[2], [1]]], 是, every_target_open_has_source_open_preimage)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0032/)

緊緻集的連續像 · qf-mod41-compactimg-continuity-audit · candidate





## 33. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-continuity-audit；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[1,2,0],"subset":[0,1,2]}。請依 [open_preimage_rows, continuous, certificate] 欄序回答。

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

Wave6第四層核對=([[[], []], [[0], [2]], [[0, 1], [0, 2]], [[0, 1, 2], [0, 1, 2]], [[0, 2], [1, 2]], [[1], [0]], [[1, 2], [0, 1]], [[2], [1]]], 是, every_target_open_has_source_open_preimage)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0033/)

緊緻集的連續像 · qf-mod41-compactimg-continuity-audit · candidate





## 34. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-continuity-audit；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[2,2,0],"subset":[0,1,2]}。請依 [open_preimage_rows, continuous, certificate] 欄序回答。

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

Wave6第四層核對=([[[], []], [[0], [2]], [[0, 1], [2]], [[0, 1, 2], [0, 1, 2]], [[0, 2], [0, 1, 2]], [[1], []], [[1, 2], [0, 1]], [[2], [0, 1]]], 是, every_target_open_has_source_open_preimage)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0034/)

緊緻集的連續像 · qf-mod41-compactimg-continuity-audit · candidate





## 35. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-continuity-audit；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[0,0,1],"subset":[0,1,2]}。請依 [open_preimage_rows, continuous, certificate] 欄序回答。

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

Wave6第四層核對=([[[], []], [[0], [0, 1]], [[0, 1], [0, 1, 2]], [[0, 1, 2], [0, 1, 2]], [[0, 2], [0, 1]], [[1], [2]], [[1, 2], [2]], [[2], []]], 是, every_target_open_has_source_open_preimage)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0035/)

緊緻集的連續像 · qf-mod41-compactimg-continuity-audit · candidate





## 36. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-continuity-audit；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[1,0,1],"subset":[0,1,2]}。請依 [open_preimage_rows, continuous, certificate] 欄序回答。

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

Wave6第四層核對=([[[], []], [[0], [1]], [[0, 1], [0, 1, 2]], [[0, 1, 2], [0, 1, 2]], [[0, 2], [1]], [[1], [0, 2]], [[1, 2], [0, 2]], [[2], []]], 是, every_target_open_has_source_open_preimage)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0036/)

緊緻集的連續像 · qf-mod41-compactimg-continuity-audit · candidate





## 37. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-continuity-audit；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[2,0,1],"subset":[0,1,2]}。請依 [open_preimage_rows, continuous, certificate] 欄序回答。

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

Wave6第四層核對=([[[], []], [[0], [1]], [[0, 1], [1, 2]], [[0, 1, 2], [0, 1, 2]], [[0, 2], [0, 1]], [[1], [2]], [[1, 2], [0, 2]], [[2], [0]]], 是, every_target_open_has_source_open_preimage)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0037/)

緊緻集的連續像 · qf-mod41-compactimg-continuity-audit · candidate





## 38. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-continuity-audit；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[0,1,1],"subset":[0,1,2]}。請依 [open_preimage_rows, continuous, certificate] 欄序回答。

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

Wave6第四層核對=([[[], []], [[0], [0]], [[0, 1], [0, 1, 2]], [[0, 1, 2], [0, 1, 2]], [[0, 2], [0]], [[1], [1, 2]], [[1, 2], [1, 2]], [[2], []]], 是, every_target_open_has_source_open_preimage)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0038/)

緊緻集的連續像 · qf-mod41-compactimg-continuity-audit · candidate





## 39. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-continuity-audit；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[1,1,1],"subset":[0,1,2]}。請依 [open_preimage_rows, continuous, certificate] 欄序回答。

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

Wave6第四層核對=([[[], []], [[0], []], [[0, 1], [0, 1, 2]], [[0, 1, 2], [0, 1, 2]], [[0, 2], []], [[1], [0, 1, 2]], [[1, 2], [0, 1, 2]], [[2], []]], 是, every_target_open_has_source_open_preimage)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0039/)

緊緻集的連續像 · qf-mod41-compactimg-continuity-audit · candidate





## 40. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-continuity-audit；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[2,1,1],"subset":[0,1,2]}。請依 [open_preimage_rows, continuous, certificate] 欄序回答。

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

Wave6第四層核對=([[[], []], [[0], []], [[0, 1], [1, 2]], [[0, 1, 2], [0, 1, 2]], [[0, 2], [0]], [[1], [1, 2]], [[1, 2], [0, 1, 2]], [[2], [0]]], 是, every_target_open_has_source_open_preimage)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0040/)

緊緻集的連續像 · qf-mod41-compactimg-continuity-audit · candidate





## 41. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-continuity-audit；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[0,2,1],"subset":[0,1,2]}。請依 [open_preimage_rows, continuous, certificate] 欄序回答。

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

Wave6第四層核對=([[[], []], [[0], [0]], [[0, 1], [0, 2]], [[0, 1, 2], [0, 1, 2]], [[0, 2], [0, 1]], [[1], [2]], [[1, 2], [1, 2]], [[2], [1]]], 是, every_target_open_has_source_open_preimage)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0041/)

緊緻集的連續像 · qf-mod41-compactimg-continuity-audit · candidate





## 42. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-continuity-audit；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[1,2,1],"subset":[0,1,2]}。請依 [open_preimage_rows, continuous, certificate] 欄序回答。

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

Wave6第四層核對=([[[], []], [[0], []], [[0, 1], [0, 2]], [[0, 1, 2], [0, 1, 2]], [[0, 2], [1]], [[1], [0, 2]], [[1, 2], [0, 1, 2]], [[2], [1]]], 是, every_target_open_has_source_open_preimage)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0042/)

緊緻集的連續像 · qf-mod41-compactimg-continuity-audit · candidate





## 43. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-continuity-audit；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[2,2,1],"subset":[0,1,2]}。請依 [open_preimage_rows, continuous, certificate] 欄序回答。

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

Wave6第四層核對=([[[], []], [[0], []], [[0, 1], [2]], [[0, 1, 2], [0, 1, 2]], [[0, 2], [0, 1]], [[1], [2]], [[1, 2], [0, 1, 2]], [[2], [0, 1]]], 是, every_target_open_has_source_open_preimage)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0043/)

緊緻集的連續像 · qf-mod41-compactimg-continuity-audit · candidate





## 44. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-continuity-audit；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[0,0,2],"subset":[0,1,2]}。請依 [open_preimage_rows, continuous, certificate] 欄序回答。

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

Wave6第四層核對=([[[], []], [[0], [0, 1]], [[0, 1], [0, 1]], [[0, 1, 2], [0, 1, 2]], [[0, 2], [0, 1, 2]], [[1], []], [[1, 2], [2]], [[2], [2]]], 是, every_target_open_has_source_open_preimage)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0044/)

緊緻集的連續像 · qf-mod41-compactimg-continuity-audit · candidate





## 45. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-continuity-audit；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[1,0,2],"subset":[0,1,2]}。請依 [open_preimage_rows, continuous, certificate] 欄序回答。

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

Wave6第四層核對=([[[], []], [[0], [1]], [[0, 1], [0, 1]], [[0, 1, 2], [0, 1, 2]], [[0, 2], [1, 2]], [[1], [0]], [[1, 2], [0, 2]], [[2], [2]]], 是, every_target_open_has_source_open_preimage)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0045/)

緊緻集的連續像 · qf-mod41-compactimg-continuity-audit · candidate





## 46. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-continuity-audit；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[2,0,2],"subset":[0,1,2]}。請依 [open_preimage_rows, continuous, certificate] 欄序回答。

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

Wave6第四層核對=([[[], []], [[0], [1]], [[0, 1], [1]], [[0, 1, 2], [0, 1, 2]], [[0, 2], [0, 1, 2]], [[1], []], [[1, 2], [0, 2]], [[2], [0, 2]]], 是, every_target_open_has_source_open_preimage)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0046/)

緊緻集的連續像 · qf-mod41-compactimg-continuity-audit · candidate





## 47. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-continuity-audit；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[0,1,2],"subset":[0,1,2]}。請依 [open_preimage_rows, continuous, certificate] 欄序回答。

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

Wave6第四層核對=([[[], []], [[0], [0]], [[0, 1], [0, 1]], [[0, 1, 2], [0, 1, 2]], [[0, 2], [0, 2]], [[1], [1]], [[1, 2], [1, 2]], [[2], [2]]], 是, every_target_open_has_source_open_preimage)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0047/)

緊緻集的連續像 · qf-mod41-compactimg-continuity-audit · candidate





## 48. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-continuity-audit；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[1,1,2],"subset":[0,1,2]}。請依 [open_preimage_rows, continuous, certificate] 欄序回答。

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

Wave6第四層核對=([[[], []], [[0], []], [[0, 1], [0, 1]], [[0, 1, 2], [0, 1, 2]], [[0, 2], [2]], [[1], [0, 1]], [[1, 2], [0, 1, 2]], [[2], [2]]], 是, every_target_open_has_source_open_preimage)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0048/)

緊緻集的連續像 · qf-mod41-compactimg-continuity-audit · candidate





## 49. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-continuity-audit；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[2,1,2],"subset":[0,1,2]}。請依 [open_preimage_rows, continuous, certificate] 欄序回答。

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

Wave6第四層核對=([[[], []], [[0], []], [[0, 1], [1]], [[0, 1, 2], [0, 1, 2]], [[0, 2], [0, 2]], [[1], [1]], [[1, 2], [0, 1, 2]], [[2], [0, 2]]], 是, every_target_open_has_source_open_preimage)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0049/)

緊緻集的連續像 · qf-mod41-compactimg-continuity-audit · candidate





## 50. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-continuity-audit；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[0,2,2],"subset":[0,1,2]}。請依 [open_preimage_rows, continuous, certificate] 欄序回答。

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

Wave6第四層核對=([[[], []], [[0], [0]], [[0, 1], [0]], [[0, 1, 2], [0, 1, 2]], [[0, 2], [0, 1, 2]], [[1], []], [[1, 2], [1, 2]], [[2], [1, 2]]], 是, every_target_open_has_source_open_preimage)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0050/)

緊緻集的連續像 · qf-mod41-compactimg-continuity-audit · candidate





## 51. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-cover-pullback；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[0,0,0],"subset":[0,1,2],"cover":[[0]]}。請依 [image, cover, relative_pullbacks, selected_indices, selected_target_opens, finite_subcover_certificate, certificate] 欄序回答。

relative_pullbacks是K內的逆像交集；selected_indices按最小數量再依遞增bitmask選首個，保留原cover索引而不聲稱唯一。

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

Wave6第四層核對=([0], [[0]], [[0, 1, 2]], [0], [[0]], 是, finite_subcover_pulled_back_to_K_then_pushed_forward_to_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0051/)

緊緻集的連續像 · qf-mod41-compactimg-cover-pullback · candidate





## 52. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-cover-pullback；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[1,0,0],"subset":[0,1,2],"cover":[[0],[1]]}。請依 [image, cover, relative_pullbacks, selected_indices, selected_target_opens, finite_subcover_certificate, certificate] 欄序回答。

relative_pullbacks是K內的逆像交集；selected_indices按最小數量再依遞增bitmask選首個，保留原cover索引而不聲稱唯一。

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

Wave6第四層核對=([0, 1], [[0], [1]], [[1, 2], [0]], [0, 1], [[0], [1]], 是, finite_subcover_pulled_back_to_K_then_pushed_forward_to_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0052/)

緊緻集的連續像 · qf-mod41-compactimg-cover-pullback · candidate





## 53. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-cover-pullback；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[2,0,0],"subset":[0,1,2],"cover":[[0],[2]]}。請依 [image, cover, relative_pullbacks, selected_indices, selected_target_opens, finite_subcover_certificate, certificate] 欄序回答。

relative_pullbacks是K內的逆像交集；selected_indices按最小數量再依遞增bitmask選首個，保留原cover索引而不聲稱唯一。

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

Wave6第四層核對=([0, 2], [[0], [2]], [[1, 2], [0]], [0, 1], [[0], [2]], 是, finite_subcover_pulled_back_to_K_then_pushed_forward_to_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0053/)

緊緻集的連續像 · qf-mod41-compactimg-cover-pullback · candidate





## 54. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-cover-pullback；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[0,1,0],"subset":[0,1,2],"cover":[[0],[1]]}。請依 [image, cover, relative_pullbacks, selected_indices, selected_target_opens, finite_subcover_certificate, certificate] 欄序回答。

relative_pullbacks是K內的逆像交集；selected_indices按最小數量再依遞增bitmask選首個，保留原cover索引而不聲稱唯一。

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

Wave6第四層核對=([0, 1], [[0], [1]], [[0, 2], [1]], [0, 1], [[0], [1]], 是, finite_subcover_pulled_back_to_K_then_pushed_forward_to_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0054/)

緊緻集的連續像 · qf-mod41-compactimg-cover-pullback · candidate





## 55. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-cover-pullback；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[1,1,0],"subset":[0,1,2],"cover":[[0],[1]]}。請依 [image, cover, relative_pullbacks, selected_indices, selected_target_opens, finite_subcover_certificate, certificate] 欄序回答。

relative_pullbacks是K內的逆像交集；selected_indices按最小數量再依遞增bitmask選首個，保留原cover索引而不聲稱唯一。

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

Wave6第四層核對=([0, 1], [[0], [1]], [[2], [0, 1]], [0, 1], [[0], [1]], 是, finite_subcover_pulled_back_to_K_then_pushed_forward_to_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0055/)

緊緻集的連續像 · qf-mod41-compactimg-cover-pullback · candidate





## 56. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-cover-pullback；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[2,1,0],"subset":[0,1,2],"cover":[[0],[1],[2]]}。請依 [image, cover, relative_pullbacks, selected_indices, selected_target_opens, finite_subcover_certificate, certificate] 欄序回答。

relative_pullbacks是K內的逆像交集；selected_indices按最小數量再依遞增bitmask選首個，保留原cover索引而不聲稱唯一。

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

Wave6第四層核對=([0, 1, 2], [[0], [1], [2]], [[2], [1], [0]], [0, 1, 2], [[0], [1], [2]], 是, finite_subcover_pulled_back_to_K_then_pushed_forward_to_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0056/)

緊緻集的連續像 · qf-mod41-compactimg-cover-pullback · candidate





## 57. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-cover-pullback；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[0,2,0],"subset":[0,1,2],"cover":[[0],[2]]}。請依 [image, cover, relative_pullbacks, selected_indices, selected_target_opens, finite_subcover_certificate, certificate] 欄序回答。

relative_pullbacks是K內的逆像交集；selected_indices按最小數量再依遞增bitmask選首個，保留原cover索引而不聲稱唯一。

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

Wave6第四層核對=([0, 2], [[0], [2]], [[0, 2], [1]], [0, 1], [[0], [2]], 是, finite_subcover_pulled_back_to_K_then_pushed_forward_to_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0057/)

緊緻集的連續像 · qf-mod41-compactimg-cover-pullback · candidate





## 58. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-cover-pullback；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[1,2,0],"subset":[0,1,2],"cover":[[0],[1],[2]]}。請依 [image, cover, relative_pullbacks, selected_indices, selected_target_opens, finite_subcover_certificate, certificate] 欄序回答。

relative_pullbacks是K內的逆像交集；selected_indices按最小數量再依遞增bitmask選首個，保留原cover索引而不聲稱唯一。

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

Wave6第四層核對=([0, 1, 2], [[0], [1], [2]], [[2], [0], [1]], [0, 1, 2], [[0], [1], [2]], 是, finite_subcover_pulled_back_to_K_then_pushed_forward_to_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0058/)

緊緻集的連續像 · qf-mod41-compactimg-cover-pullback · candidate





## 59. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-cover-pullback；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[2,2,0],"subset":[0,1,2],"cover":[[0],[2]]}。請依 [image, cover, relative_pullbacks, selected_indices, selected_target_opens, finite_subcover_certificate, certificate] 欄序回答。

relative_pullbacks是K內的逆像交集；selected_indices按最小數量再依遞增bitmask選首個，保留原cover索引而不聲稱唯一。

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

Wave6第四層核對=([0, 2], [[0], [2]], [[2], [0, 1]], [0, 1], [[0], [2]], 是, finite_subcover_pulled_back_to_K_then_pushed_forward_to_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0059/)

緊緻集的連續像 · qf-mod41-compactimg-cover-pullback · candidate





## 60. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-cover-pullback；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[0,0,1],"subset":[0,1,2],"cover":[[0],[1]]}。請依 [image, cover, relative_pullbacks, selected_indices, selected_target_opens, finite_subcover_certificate, certificate] 欄序回答。

relative_pullbacks是K內的逆像交集；selected_indices按最小數量再依遞增bitmask選首個，保留原cover索引而不聲稱唯一。

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

Wave6第四層核對=([0, 1], [[0], [1]], [[0, 1], [2]], [0, 1], [[0], [1]], 是, finite_subcover_pulled_back_to_K_then_pushed_forward_to_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0060/)

緊緻集的連續像 · qf-mod41-compactimg-cover-pullback · candidate





## 61. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-cover-pullback；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[1,0,1],"subset":[0,1,2],"cover":[[0],[1]]}。請依 [image, cover, relative_pullbacks, selected_indices, selected_target_opens, finite_subcover_certificate, certificate] 欄序回答。

relative_pullbacks是K內的逆像交集；selected_indices按最小數量再依遞增bitmask選首個，保留原cover索引而不聲稱唯一。

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

Wave6第四層核對=([0, 1], [[0], [1]], [[1], [0, 2]], [0, 1], [[0], [1]], 是, finite_subcover_pulled_back_to_K_then_pushed_forward_to_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0061/)

緊緻集的連續像 · qf-mod41-compactimg-cover-pullback · candidate





## 62. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-cover-pullback；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[2,0,1],"subset":[0,1,2],"cover":[[0],[1],[2]]}。請依 [image, cover, relative_pullbacks, selected_indices, selected_target_opens, finite_subcover_certificate, certificate] 欄序回答。

relative_pullbacks是K內的逆像交集；selected_indices按最小數量再依遞增bitmask選首個，保留原cover索引而不聲稱唯一。

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

Wave6第四層核對=([0, 1, 2], [[0], [1], [2]], [[1], [2], [0]], [0, 1, 2], [[0], [1], [2]], 是, finite_subcover_pulled_back_to_K_then_pushed_forward_to_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0062/)

緊緻集的連續像 · qf-mod41-compactimg-cover-pullback · candidate





## 63. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-cover-pullback；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[0,1,1],"subset":[0,1,2],"cover":[[0],[1]]}。請依 [image, cover, relative_pullbacks, selected_indices, selected_target_opens, finite_subcover_certificate, certificate] 欄序回答。

relative_pullbacks是K內的逆像交集；selected_indices按最小數量再依遞增bitmask選首個，保留原cover索引而不聲稱唯一。

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

Wave6第四層核對=([0, 1], [[0], [1]], [[0], [1, 2]], [0, 1], [[0], [1]], 是, finite_subcover_pulled_back_to_K_then_pushed_forward_to_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0063/)

緊緻集的連續像 · qf-mod41-compactimg-cover-pullback · candidate





## 64. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-cover-pullback；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[1,1,1],"subset":[0,1,2],"cover":[[1]]}。請依 [image, cover, relative_pullbacks, selected_indices, selected_target_opens, finite_subcover_certificate, certificate] 欄序回答。

relative_pullbacks是K內的逆像交集；selected_indices按最小數量再依遞增bitmask選首個，保留原cover索引而不聲稱唯一。

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

Wave6第四層核對=([1], [[1]], [[0, 1, 2]], [0], [[1]], 是, finite_subcover_pulled_back_to_K_then_pushed_forward_to_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0064/)

緊緻集的連續像 · qf-mod41-compactimg-cover-pullback · candidate





## 65. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-cover-pullback；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[2,1,1],"subset":[0,1,2],"cover":[[1],[2]]}。請依 [image, cover, relative_pullbacks, selected_indices, selected_target_opens, finite_subcover_certificate, certificate] 欄序回答。

relative_pullbacks是K內的逆像交集；selected_indices按最小數量再依遞增bitmask選首個，保留原cover索引而不聲稱唯一。

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

Wave6第四層核對=([1, 2], [[1], [2]], [[1, 2], [0]], [0, 1], [[1], [2]], 是, finite_subcover_pulled_back_to_K_then_pushed_forward_to_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0065/)

緊緻集的連續像 · qf-mod41-compactimg-cover-pullback · candidate





## 66. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-cover-pullback；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[0,2,1],"subset":[0,1,2],"cover":[[0],[1],[2]]}。請依 [image, cover, relative_pullbacks, selected_indices, selected_target_opens, finite_subcover_certificate, certificate] 欄序回答。

relative_pullbacks是K內的逆像交集；selected_indices按最小數量再依遞增bitmask選首個，保留原cover索引而不聲稱唯一。

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

Wave6第四層核對=([0, 1, 2], [[0], [1], [2]], [[0], [2], [1]], [0, 1, 2], [[0], [1], [2]], 是, finite_subcover_pulled_back_to_K_then_pushed_forward_to_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0066/)

緊緻集的連續像 · qf-mod41-compactimg-cover-pullback · candidate





## 67. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-cover-pullback；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[1,2,1],"subset":[0,1,2],"cover":[[1],[2]]}。請依 [image, cover, relative_pullbacks, selected_indices, selected_target_opens, finite_subcover_certificate, certificate] 欄序回答。

relative_pullbacks是K內的逆像交集；selected_indices按最小數量再依遞增bitmask選首個，保留原cover索引而不聲稱唯一。

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

Wave6第四層核對=([1, 2], [[1], [2]], [[0, 2], [1]], [0, 1], [[1], [2]], 是, finite_subcover_pulled_back_to_K_then_pushed_forward_to_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0067/)

緊緻集的連續像 · qf-mod41-compactimg-cover-pullback · candidate





## 68. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-cover-pullback；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[2,2,1],"subset":[0,1,2],"cover":[[1],[2]]}。請依 [image, cover, relative_pullbacks, selected_indices, selected_target_opens, finite_subcover_certificate, certificate] 欄序回答。

relative_pullbacks是K內的逆像交集；selected_indices按最小數量再依遞增bitmask選首個，保留原cover索引而不聲稱唯一。

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

Wave6第四層核對=([1, 2], [[1], [2]], [[2], [0, 1]], [0, 1], [[1], [2]], 是, finite_subcover_pulled_back_to_K_then_pushed_forward_to_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0068/)

緊緻集的連續像 · qf-mod41-compactimg-cover-pullback · candidate





## 69. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-cover-pullback；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[0,0,2],"subset":[0,1,2],"cover":[[0],[2]]}。請依 [image, cover, relative_pullbacks, selected_indices, selected_target_opens, finite_subcover_certificate, certificate] 欄序回答。

relative_pullbacks是K內的逆像交集；selected_indices按最小數量再依遞增bitmask選首個，保留原cover索引而不聲稱唯一。

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

Wave6第四層核對=([0, 2], [[0], [2]], [[0, 1], [2]], [0, 1], [[0], [2]], 是, finite_subcover_pulled_back_to_K_then_pushed_forward_to_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0069/)

緊緻集的連續像 · qf-mod41-compactimg-cover-pullback · candidate





## 70. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-cover-pullback；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[1,0,2],"subset":[0,1,2],"cover":[[0],[1],[2]]}。請依 [image, cover, relative_pullbacks, selected_indices, selected_target_opens, finite_subcover_certificate, certificate] 欄序回答。

relative_pullbacks是K內的逆像交集；selected_indices按最小數量再依遞增bitmask選首個，保留原cover索引而不聲稱唯一。

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

Wave6第四層核對=([0, 1, 2], [[0], [1], [2]], [[1], [0], [2]], [0, 1, 2], [[0], [1], [2]], 是, finite_subcover_pulled_back_to_K_then_pushed_forward_to_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0070/)

緊緻集的連續像 · qf-mod41-compactimg-cover-pullback · candidate





## 71. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-cover-pullback；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[2,0,2],"subset":[0,1,2],"cover":[[0],[2]]}。請依 [image, cover, relative_pullbacks, selected_indices, selected_target_opens, finite_subcover_certificate, certificate] 欄序回答。

relative_pullbacks是K內的逆像交集；selected_indices按最小數量再依遞增bitmask選首個，保留原cover索引而不聲稱唯一。

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

Wave6第四層核對=([0, 2], [[0], [2]], [[1], [0, 2]], [0, 1], [[0], [2]], 是, finite_subcover_pulled_back_to_K_then_pushed_forward_to_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0071/)

緊緻集的連續像 · qf-mod41-compactimg-cover-pullback · candidate





## 72. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-cover-pullback；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[0,1,2],"subset":[0,1,2],"cover":[[0],[1],[2]]}。請依 [image, cover, relative_pullbacks, selected_indices, selected_target_opens, finite_subcover_certificate, certificate] 欄序回答。

relative_pullbacks是K內的逆像交集；selected_indices按最小數量再依遞增bitmask選首個，保留原cover索引而不聲稱唯一。

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

Wave6第四層核對=([0, 1, 2], [[0], [1], [2]], [[0], [1], [2]], [0, 1, 2], [[0], [1], [2]], 是, finite_subcover_pulled_back_to_K_then_pushed_forward_to_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0072/)

緊緻集的連續像 · qf-mod41-compactimg-cover-pullback · candidate





## 73. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-cover-pullback；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[1,1,2],"subset":[0,1,2],"cover":[[1],[2]]}。請依 [image, cover, relative_pullbacks, selected_indices, selected_target_opens, finite_subcover_certificate, certificate] 欄序回答。

relative_pullbacks是K內的逆像交集；selected_indices按最小數量再依遞增bitmask選首個，保留原cover索引而不聲稱唯一。

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

Wave6第四層核對=([1, 2], [[1], [2]], [[0, 1], [2]], [0, 1], [[1], [2]], 是, finite_subcover_pulled_back_to_K_then_pushed_forward_to_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0073/)

緊緻集的連續像 · qf-mod41-compactimg-cover-pullback · candidate





## 74. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-cover-pullback；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[2,1,2],"subset":[0,1,2],"cover":[[1],[2]]}。請依 [image, cover, relative_pullbacks, selected_indices, selected_target_opens, finite_subcover_certificate, certificate] 欄序回答。

relative_pullbacks是K內的逆像交集；selected_indices按最小數量再依遞增bitmask選首個，保留原cover索引而不聲稱唯一。

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

Wave6第四層核對=([1, 2], [[1], [2]], [[1], [0, 2]], [0, 1], [[1], [2]], 是, finite_subcover_pulled_back_to_K_then_pushed_forward_to_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0074/)

緊緻集的連續像 · qf-mod41-compactimg-cover-pullback · candidate





## 75. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-cover-pullback；資料={"source_n":3,"target_n":3,"source_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"target_topology":[[],[0],[0,1],[0,1,2],[0,2],[1],[1,2],[2]],"map":[0,2,2],"subset":[0,1,2],"cover":[[0],[2]]}。請依 [image, cover, relative_pullbacks, selected_indices, selected_target_opens, finite_subcover_certificate, certificate] 欄序回答。

relative_pullbacks是K內的逆像交集；selected_indices按最小數量再依遞增bitmask選首個，保留原cover索引而不聲稱唯一。

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

Wave6第四層核對=([0, 2], [[0], [2]], [[0], [1, 2]], [0, 1], [[0], [2]], 是, finite_subcover_pulled_back_to_K_then_pushed_forward_to_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0075/)

緊緻集的連續像 · qf-mod41-compactimg-cover-pullback · candidate





## 76. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-reverse-implication-boundary；資料={"left":-2,"right":2,"value":0}。請依 [left, right, constant_value, domain_compact, continuous, image_compact, reverse_implication_claim, boundary] 欄序回答。

查看答案與解釋(-2, 2, 0, 否, 是, 是, 否, constant_continuous_map_from_noncompact_open_interval_has_compact_singleton_image)

Wave6第四層核對=(-2, 2, 0, 否, 是, 是, 否, constant_continuous_map_from_noncompact_open_interval_has_compact_singleton_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0076/)

緊緻集的連續像 · qf-mod41-compactimg-reverse-implication-boundary · candidate





## 77. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-reverse-implication-boundary；資料={"left":-3,"right":3,"value":1}。請依 [left, right, constant_value, domain_compact, continuous, image_compact, reverse_implication_claim, boundary] 欄序回答。

查看答案與解釋(-3, 3, 1, 否, 是, 是, 否, constant_continuous_map_from_noncompact_open_interval_has_compact_singleton_image)

Wave6第四層核對=(-3, 3, 1, 否, 是, 是, 否, constant_continuous_map_from_noncompact_open_interval_has_compact_singleton_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0077/)

緊緻集的連續像 · qf-mod41-compactimg-reverse-implication-boundary · candidate





## 78. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-reverse-implication-boundary；資料={"left":-4,"right":4,"value":2}。請依 [left, right, constant_value, domain_compact, continuous, image_compact, reverse_implication_claim, boundary] 欄序回答。

查看答案與解釋(-4, 4, 2, 否, 是, 是, 否, constant_continuous_map_from_noncompact_open_interval_has_compact_singleton_image)

Wave6第四層核對=(-4, 4, 2, 否, 是, 是, 否, constant_continuous_map_from_noncompact_open_interval_has_compact_singleton_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0078/)

緊緻集的連續像 · qf-mod41-compactimg-reverse-implication-boundary · candidate





## 79. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-reverse-implication-boundary；資料={"left":-5,"right":5,"value":3}。請依 [left, right, constant_value, domain_compact, continuous, image_compact, reverse_implication_claim, boundary] 欄序回答。

查看答案與解釋(-5, 5, 3, 否, 是, 是, 否, constant_continuous_map_from_noncompact_open_interval_has_compact_singleton_image)

Wave6第四層核對=(-5, 5, 3, 否, 是, 是, 否, constant_continuous_map_from_noncompact_open_interval_has_compact_singleton_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0079/)

緊緻集的連續像 · qf-mod41-compactimg-reverse-implication-boundary · candidate





## 80. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-reverse-implication-boundary；資料={"left":-6,"right":6,"value":4}。請依 [left, right, constant_value, domain_compact, continuous, image_compact, reverse_implication_claim, boundary] 欄序回答。

查看答案與解釋(-6, 6, 4, 否, 是, 是, 否, constant_continuous_map_from_noncompact_open_interval_has_compact_singleton_image)

Wave6第四層核對=(-6, 6, 4, 否, 是, 是, 否, constant_continuous_map_from_noncompact_open_interval_has_compact_singleton_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0080/)

緊緻集的連續像 · qf-mod41-compactimg-reverse-implication-boundary · candidate





## 81. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-reverse-implication-boundary；資料={"left":-7,"right":7,"value":5}。請依 [left, right, constant_value, domain_compact, continuous, image_compact, reverse_implication_claim, boundary] 欄序回答。

查看答案與解釋(-7, 7, 5, 否, 是, 是, 否, constant_continuous_map_from_noncompact_open_interval_has_compact_singleton_image)

Wave6第四層核對=(-7, 7, 5, 否, 是, 是, 否, constant_continuous_map_from_noncompact_open_interval_has_compact_singleton_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0081/)

緊緻集的連續像 · qf-mod41-compactimg-reverse-implication-boundary · candidate





## 82. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-reverse-implication-boundary；資料={"left":-8,"right":8,"value":6}。請依 [left, right, constant_value, domain_compact, continuous, image_compact, reverse_implication_claim, boundary] 欄序回答。

查看答案與解釋(-8, 8, 6, 否, 是, 是, 否, constant_continuous_map_from_noncompact_open_interval_has_compact_singleton_image)

Wave6第四層核對=(-8, 8, 6, 否, 是, 是, 否, constant_continuous_map_from_noncompact_open_interval_has_compact_singleton_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0082/)

緊緻集的連續像 · qf-mod41-compactimg-reverse-implication-boundary · candidate





## 83. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-reverse-implication-boundary；資料={"left":-9,"right":9,"value":7}。請依 [left, right, constant_value, domain_compact, continuous, image_compact, reverse_implication_claim, boundary] 欄序回答。

查看答案與解釋(-9, 9, 7, 否, 是, 是, 否, constant_continuous_map_from_noncompact_open_interval_has_compact_singleton_image)

Wave6第四層核對=(-9, 9, 7, 否, 是, 是, 否, constant_continuous_map_from_noncompact_open_interval_has_compact_singleton_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0083/)

緊緻集的連續像 · qf-mod41-compactimg-reverse-implication-boundary · candidate





## 84. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-reverse-implication-boundary；資料={"left":-10,"right":10,"value":8}。請依 [left, right, constant_value, domain_compact, continuous, image_compact, reverse_implication_claim, boundary] 欄序回答。

查看答案與解釋(-10, 10, 8, 否, 是, 是, 否, constant_continuous_map_from_noncompact_open_interval_has_compact_singleton_image)

Wave6第四層核對=(-10, 10, 8, 否, 是, 是, 否, constant_continuous_map_from_noncompact_open_interval_has_compact_singleton_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0084/)

緊緻集的連續像 · qf-mod41-compactimg-reverse-implication-boundary · candidate





## 85. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-reverse-implication-boundary；資料={"left":-11,"right":11,"value":9}。請依 [left, right, constant_value, domain_compact, continuous, image_compact, reverse_implication_claim, boundary] 欄序回答。

查看答案與解釋(-11, 11, 9, 否, 是, 是, 否, constant_continuous_map_from_noncompact_open_interval_has_compact_singleton_image)

Wave6第四層核對=(-11, 11, 9, 否, 是, 是, 否, constant_continuous_map_from_noncompact_open_interval_has_compact_singleton_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0085/)

緊緻集的連續像 · qf-mod41-compactimg-reverse-implication-boundary · candidate





## 86. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-reverse-implication-boundary；資料={"left":-12,"right":12,"value":10}。請依 [left, right, constant_value, domain_compact, continuous, image_compact, reverse_implication_claim, boundary] 欄序回答。

查看答案與解釋(-12, 12, 10, 否, 是, 是, 否, constant_continuous_map_from_noncompact_open_interval_has_compact_singleton_image)

Wave6第四層核對=(-12, 12, 10, 否, 是, 是, 否, constant_continuous_map_from_noncompact_open_interval_has_compact_singleton_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0086/)

緊緻集的連續像 · qf-mod41-compactimg-reverse-implication-boundary · candidate





## 87. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-reverse-implication-boundary；資料={"left":-13,"right":13,"value":11}。請依 [left, right, constant_value, domain_compact, continuous, image_compact, reverse_implication_claim, boundary] 欄序回答。

查看答案與解釋(-13, 13, 11, 否, 是, 是, 否, constant_continuous_map_from_noncompact_open_interval_has_compact_singleton_image)

Wave6第四層核對=(-13, 13, 11, 否, 是, 是, 否, constant_continuous_map_from_noncompact_open_interval_has_compact_singleton_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0087/)

緊緻集的連續像 · qf-mod41-compactimg-reverse-implication-boundary · candidate





## 88. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-reverse-implication-boundary；資料={"left":-14,"right":14,"value":12}。請依 [left, right, constant_value, domain_compact, continuous, image_compact, reverse_implication_claim, boundary] 欄序回答。

查看答案與解釋(-14, 14, 12, 否, 是, 是, 否, constant_continuous_map_from_noncompact_open_interval_has_compact_singleton_image)

Wave6第四層核對=(-14, 14, 12, 否, 是, 是, 否, constant_continuous_map_from_noncompact_open_interval_has_compact_singleton_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0088/)

緊緻集的連續像 · qf-mod41-compactimg-reverse-implication-boundary · candidate





## 89. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-reverse-implication-boundary；資料={"left":-15,"right":15,"value":13}。請依 [left, right, constant_value, domain_compact, continuous, image_compact, reverse_implication_claim, boundary] 欄序回答。

查看答案與解釋(-15, 15, 13, 否, 是, 是, 否, constant_continuous_map_from_noncompact_open_interval_has_compact_singleton_image)

Wave6第四層核對=(-15, 15, 13, 否, 是, 是, 否, constant_continuous_map_from_noncompact_open_interval_has_compact_singleton_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0089/)

緊緻集的連續像 · qf-mod41-compactimg-reverse-implication-boundary · candidate





## 90. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-reverse-implication-boundary；資料={"left":-16,"right":16,"value":14}。請依 [left, right, constant_value, domain_compact, continuous, image_compact, reverse_implication_claim, boundary] 欄序回答。

查看答案與解釋(-16, 16, 14, 否, 是, 是, 否, constant_continuous_map_from_noncompact_open_interval_has_compact_singleton_image)

Wave6第四層核對=(-16, 16, 14, 否, 是, 是, 否, constant_continuous_map_from_noncompact_open_interval_has_compact_singleton_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0090/)

緊緻集的連續像 · qf-mod41-compactimg-reverse-implication-boundary · candidate





## 91. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-reverse-implication-boundary；資料={"left":-17,"right":17,"value":15}。請依 [left, right, constant_value, domain_compact, continuous, image_compact, reverse_implication_claim, boundary] 欄序回答。

查看答案與解釋(-17, 17, 15, 否, 是, 是, 否, constant_continuous_map_from_noncompact_open_interval_has_compact_singleton_image)

Wave6第四層核對=(-17, 17, 15, 否, 是, 是, 否, constant_continuous_map_from_noncompact_open_interval_has_compact_singleton_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0091/)

緊緻集的連續像 · qf-mod41-compactimg-reverse-implication-boundary · candidate





## 92. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-reverse-implication-boundary；資料={"left":-18,"right":18,"value":16}。請依 [left, right, constant_value, domain_compact, continuous, image_compact, reverse_implication_claim, boundary] 欄序回答。

查看答案與解釋(-18, 18, 16, 否, 是, 是, 否, constant_continuous_map_from_noncompact_open_interval_has_compact_singleton_image)

Wave6第四層核對=(-18, 18, 16, 否, 是, 是, 否, constant_continuous_map_from_noncompact_open_interval_has_compact_singleton_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0092/)

緊緻集的連續像 · qf-mod41-compactimg-reverse-implication-boundary · candidate





## 93. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-reverse-implication-boundary；資料={"left":-19,"right":19,"value":17}。請依 [left, right, constant_value, domain_compact, continuous, image_compact, reverse_implication_claim, boundary] 欄序回答。

查看答案與解釋(-19, 19, 17, 否, 是, 是, 否, constant_continuous_map_from_noncompact_open_interval_has_compact_singleton_image)

Wave6第四層核對=(-19, 19, 17, 否, 是, 是, 否, constant_continuous_map_from_noncompact_open_interval_has_compact_singleton_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0093/)

緊緻集的連續像 · qf-mod41-compactimg-reverse-implication-boundary · candidate





## 94. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-reverse-implication-boundary；資料={"left":-20,"right":20,"value":18}。請依 [left, right, constant_value, domain_compact, continuous, image_compact, reverse_implication_claim, boundary] 欄序回答。

查看答案與解釋(-20, 20, 18, 否, 是, 是, 否, constant_continuous_map_from_noncompact_open_interval_has_compact_singleton_image)

Wave6第四層核對=(-20, 20, 18, 否, 是, 是, 否, constant_continuous_map_from_noncompact_open_interval_has_compact_singleton_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0094/)

緊緻集的連續像 · qf-mod41-compactimg-reverse-implication-boundary · candidate





## 95. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-reverse-implication-boundary；資料={"left":-21,"right":21,"value":19}。請依 [left, right, constant_value, domain_compact, continuous, image_compact, reverse_implication_claim, boundary] 欄序回答。

查看答案與解釋(-21, 21, 19, 否, 是, 是, 否, constant_continuous_map_from_noncompact_open_interval_has_compact_singleton_image)

Wave6第四層核對=(-21, 21, 19, 否, 是, 是, 否, constant_continuous_map_from_noncompact_open_interval_has_compact_singleton_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0095/)

緊緻集的連續像 · qf-mod41-compactimg-reverse-implication-boundary · candidate





## 96. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-reverse-implication-boundary；資料={"left":-22,"right":22,"value":20}。請依 [left, right, constant_value, domain_compact, continuous, image_compact, reverse_implication_claim, boundary] 欄序回答。

查看答案與解釋(-22, 22, 20, 否, 是, 是, 否, constant_continuous_map_from_noncompact_open_interval_has_compact_singleton_image)

Wave6第四層核對=(-22, 22, 20, 否, 是, 是, 否, constant_continuous_map_from_noncompact_open_interval_has_compact_singleton_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0096/)

緊緻集的連續像 · qf-mod41-compactimg-reverse-implication-boundary · candidate





## 97. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-reverse-implication-boundary；資料={"left":-23,"right":23,"value":21}。請依 [left, right, constant_value, domain_compact, continuous, image_compact, reverse_implication_claim, boundary] 欄序回答。

查看答案與解釋(-23, 23, 21, 否, 是, 是, 否, constant_continuous_map_from_noncompact_open_interval_has_compact_singleton_image)

Wave6第四層核對=(-23, 23, 21, 否, 是, 是, 否, constant_continuous_map_from_noncompact_open_interval_has_compact_singleton_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0097/)

緊緻集的連續像 · qf-mod41-compactimg-reverse-implication-boundary · candidate





## 98. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-reverse-implication-boundary；資料={"left":-24,"right":24,"value":22}。請依 [left, right, constant_value, domain_compact, continuous, image_compact, reverse_implication_claim, boundary] 欄序回答。

查看答案與解釋(-24, 24, 22, 否, 是, 是, 否, constant_continuous_map_from_noncompact_open_interval_has_compact_singleton_image)

Wave6第四層核對=(-24, 24, 22, 否, 是, 是, 否, constant_continuous_map_from_noncompact_open_interval_has_compact_singleton_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0098/)

緊緻集的連續像 · qf-mod41-compactimg-reverse-implication-boundary · candidate





## 99. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-reverse-implication-boundary；資料={"left":-25,"right":25,"value":23}。請依 [left, right, constant_value, domain_compact, continuous, image_compact, reverse_implication_claim, boundary] 欄序回答。

查看答案與解釋(-25, 25, 23, 否, 是, 是, 否, constant_continuous_map_from_noncompact_open_interval_has_compact_singleton_image)

Wave6第四層核對=(-25, 25, 23, 否, 是, 是, 否, constant_continuous_map_from_noncompact_open_interval_has_compact_singleton_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0099/)

緊緻集的連續像 · qf-mod41-compactimg-reverse-implication-boundary · candidate





## 100. 緊緻集的連續像

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-reverse-implication-boundary；資料={"left":-26,"right":26,"value":24}。請依 [left, right, constant_value, domain_compact, continuous, image_compact, reverse_implication_claim, boundary] 欄序回答。

查看答案與解釋(-26, 26, 24, 否, 是, 是, 否, constant_continuous_map_from_noncompact_open_interval_has_compact_singleton_image)

Wave6第四層核對=(-26, 26, 24, 否, 是, 是, 否, constant_continuous_map_from_noncompact_open_interval_has_compact_singleton_image)；依完整明示資料獨立重算；對image open cover先拉回K取得finite subcover再推回image；不需injective或surjective；compact image不反推domain compact，preimage compact與image closed皆需額外假設。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r03-continuous-image-of-compact-0100/)

緊緻集的連續像 · qf-mod41-compactimg-reverse-implication-boundary · candidate



[原始題目 JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261014-advance-20261110-r03-continuous-image-of-compact-foundations/questions.jsonl) · [驗收報告](https://ocme.evemisslab.com/data/questions/batches/batch-20261014-advance-20261110-r03-continuous-image-of-compact-foundations/validation-report.json)