# 商拓撲基礎 · 脈衝 R05

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

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

batch-20261015-advance-20261117-r05-quotient-topology-foundations · 2026-10-15 · 100 題

欄序為來源綁定的呈現補充；原始 JSONL 與數學答案不變。

[欄序與來源綁定資料](https://ocme.evemisslab.com/data/i18n/question-output-protocols.json)



## 1. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-fibers；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1]],"y_points":["a","b"],"q_map":["a","a","b","b","b","b"]}。請依 [fibers, surjective, fiber_cover, certificate] 欄序回答。

查看答案與解釋([[a, [0, 1]], [b, [2, 3, 4, 5]]], 是, 是, fibers_partition_X)

Wave6第十一層核對=([[a, [0, 1]], [b, [2, 3, 4, 5]]], 是, 是, fibers_partition_X)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0001/)

商拓撲 · qf-mod48-quotient-fibers · candidate





## 2. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-fibers；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,2]],"y_points":["a","b"],"q_map":["a","b","a","b","b","b"]}。請依 [fibers, surjective, fiber_cover, certificate] 欄序回答。

查看答案與解釋([[a, [0, 2]], [b, [1, 3, 4, 5]]], 是, 是, fibers_partition_X)

Wave6第十一層核對=([[a, [0, 2]], [b, [1, 3, 4, 5]]], 是, 是, fibers_partition_X)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0002/)

商拓撲 · qf-mod48-quotient-fibers · candidate





## 3. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-fibers；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,2]],"y_points":["a","b"],"q_map":["a","a","a","b","b","b"]}。請依 [fibers, surjective, fiber_cover, certificate] 欄序回答。

查看答案與解釋([[a, [0, 1, 2]], [b, [3, 4, 5]]], 是, 是, fibers_partition_X)

Wave6第十一層核對=([[a, [0, 1, 2]], [b, [3, 4, 5]]], 是, 是, fibers_partition_X)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0003/)

商拓撲 · qf-mod48-quotient-fibers · candidate





## 4. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-fibers；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,3]],"y_points":["a","b"],"q_map":["a","b","b","a","b","b"]}。請依 [fibers, surjective, fiber_cover, certificate] 欄序回答。

查看答案與解釋([[a, [0, 3]], [b, [1, 2, 4, 5]]], 是, 是, fibers_partition_X)

Wave6第十一層核對=([[a, [0, 3]], [b, [1, 2, 4, 5]]], 是, 是, fibers_partition_X)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0004/)

商拓撲 · qf-mod48-quotient-fibers · candidate





## 5. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-fibers；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,3]],"y_points":["a","b"],"q_map":["a","a","b","a","b","b"]}。請依 [fibers, surjective, fiber_cover, certificate] 欄序回答。

查看答案與解釋([[a, [0, 1, 3]], [b, [2, 4, 5]]], 是, 是, fibers_partition_X)

Wave6第十一層核對=([[a, [0, 1, 3]], [b, [2, 4, 5]]], 是, 是, fibers_partition_X)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0005/)

商拓撲 · qf-mod48-quotient-fibers · candidate





## 6. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-fibers；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,2,3]],"y_points":["a","b"],"q_map":["a","b","a","a","b","b"]}。請依 [fibers, surjective, fiber_cover, certificate] 欄序回答。

查看答案與解釋([[a, [0, 2, 3]], [b, [1, 4, 5]]], 是, 是, fibers_partition_X)

Wave6第十一層核對=([[a, [0, 2, 3]], [b, [1, 4, 5]]], 是, 是, fibers_partition_X)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0006/)

商拓撲 · qf-mod48-quotient-fibers · candidate





## 7. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-fibers；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,2,3]],"y_points":["a","b"],"q_map":["a","a","a","a","b","b"]}。請依 [fibers, surjective, fiber_cover, certificate] 欄序回答。

查看答案與解釋([[a, [0, 1, 2, 3]], [b, [4, 5]]], 是, 是, fibers_partition_X)

Wave6第十一層核對=([[a, [0, 1, 2, 3]], [b, [4, 5]]], 是, 是, fibers_partition_X)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0007/)

商拓撲 · qf-mod48-quotient-fibers · candidate





## 8. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-fibers；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,4]],"y_points":["a","b"],"q_map":["a","b","b","b","a","b"]}。請依 [fibers, surjective, fiber_cover, certificate] 欄序回答。

查看答案與解釋([[a, [0, 4]], [b, [1, 2, 3, 5]]], 是, 是, fibers_partition_X)

Wave6第十一層核對=([[a, [0, 4]], [b, [1, 2, 3, 5]]], 是, 是, fibers_partition_X)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0008/)

商拓撲 · qf-mod48-quotient-fibers · candidate





## 9. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-fibers；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,4]],"y_points":["a","b"],"q_map":["a","a","b","b","a","b"]}。請依 [fibers, surjective, fiber_cover, certificate] 欄序回答。

查看答案與解釋([[a, [0, 1, 4]], [b, [2, 3, 5]]], 是, 是, fibers_partition_X)

Wave6第十一層核對=([[a, [0, 1, 4]], [b, [2, 3, 5]]], 是, 是, fibers_partition_X)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0009/)

商拓撲 · qf-mod48-quotient-fibers · candidate





## 10. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-fibers；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,2,4]],"y_points":["a","b"],"q_map":["a","b","a","b","a","b"]}。請依 [fibers, surjective, fiber_cover, certificate] 欄序回答。

查看答案與解釋([[a, [0, 2, 4]], [b, [1, 3, 5]]], 是, 是, fibers_partition_X)

Wave6第十一層核對=([[a, [0, 2, 4]], [b, [1, 3, 5]]], 是, 是, fibers_partition_X)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0010/)

商拓撲 · qf-mod48-quotient-fibers · candidate





## 11. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-fibers；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,2,4]],"y_points":["a","b"],"q_map":["a","a","a","b","a","b"]}。請依 [fibers, surjective, fiber_cover, certificate] 欄序回答。

查看答案與解釋([[a, [0, 1, 2, 4]], [b, [3, 5]]], 是, 是, fibers_partition_X)

Wave6第十一層核對=([[a, [0, 1, 2, 4]], [b, [3, 5]]], 是, 是, fibers_partition_X)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0011/)

商拓撲 · qf-mod48-quotient-fibers · candidate





## 12. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-fibers；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,3,4]],"y_points":["a","b"],"q_map":["a","b","b","a","a","b"]}。請依 [fibers, surjective, fiber_cover, certificate] 欄序回答。

查看答案與解釋([[a, [0, 3, 4]], [b, [1, 2, 5]]], 是, 是, fibers_partition_X)

Wave6第十一層核對=([[a, [0, 3, 4]], [b, [1, 2, 5]]], 是, 是, fibers_partition_X)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0012/)

商拓撲 · qf-mod48-quotient-fibers · candidate





## 13. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-fibers；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,3,4]],"y_points":["a","b"],"q_map":["a","a","b","a","a","b"]}。請依 [fibers, surjective, fiber_cover, certificate] 欄序回答。

查看答案與解釋([[a, [0, 1, 3, 4]], [b, [2, 5]]], 是, 是, fibers_partition_X)

Wave6第十一層核對=([[a, [0, 1, 3, 4]], [b, [2, 5]]], 是, 是, fibers_partition_X)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0013/)

商拓撲 · qf-mod48-quotient-fibers · candidate





## 14. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-fibers；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,2,3,4]],"y_points":["a","b"],"q_map":["a","b","a","a","a","b"]}。請依 [fibers, surjective, fiber_cover, certificate] 欄序回答。

查看答案與解釋([[a, [0, 2, 3, 4]], [b, [1, 5]]], 是, 是, fibers_partition_X)

Wave6第十一層核對=([[a, [0, 2, 3, 4]], [b, [1, 5]]], 是, 是, fibers_partition_X)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0014/)

商拓撲 · qf-mod48-quotient-fibers · candidate





## 15. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-fibers；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,2,3,4]],"y_points":["a","b"],"q_map":["a","a","a","a","a","b"]}。請依 [fibers, surjective, fiber_cover, certificate] 欄序回答。

查看答案與解釋([[a, [0, 1, 2, 3, 4]], [b, [5]]], 是, 是, fibers_partition_X)

Wave6第十一層核對=([[a, [0, 1, 2, 3, 4]], [b, [5]]], 是, 是, fibers_partition_X)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0015/)

商拓撲 · qf-mod48-quotient-fibers · candidate





## 16. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-fibers；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,5]],"y_points":["a","b"],"q_map":["a","b","b","b","b","a"]}。請依 [fibers, surjective, fiber_cover, certificate] 欄序回答。

查看答案與解釋([[a, [0, 5]], [b, [1, 2, 3, 4]]], 是, 是, fibers_partition_X)

Wave6第十一層核對=([[a, [0, 5]], [b, [1, 2, 3, 4]]], 是, 是, fibers_partition_X)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0016/)

商拓撲 · qf-mod48-quotient-fibers · candidate





## 17. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-fibers；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,5]],"y_points":["a","b"],"q_map":["a","a","b","b","b","a"]}。請依 [fibers, surjective, fiber_cover, certificate] 欄序回答。

查看答案與解釋([[a, [0, 1, 5]], [b, [2, 3, 4]]], 是, 是, fibers_partition_X)

Wave6第十一層核對=([[a, [0, 1, 5]], [b, [2, 3, 4]]], 是, 是, fibers_partition_X)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0017/)

商拓撲 · qf-mod48-quotient-fibers · candidate





## 18. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-fibers；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,2,5]],"y_points":["a","b"],"q_map":["a","b","a","b","b","a"]}。請依 [fibers, surjective, fiber_cover, certificate] 欄序回答。

查看答案與解釋([[a, [0, 2, 5]], [b, [1, 3, 4]]], 是, 是, fibers_partition_X)

Wave6第十一層核對=([[a, [0, 2, 5]], [b, [1, 3, 4]]], 是, 是, fibers_partition_X)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0018/)

商拓撲 · qf-mod48-quotient-fibers · candidate





## 19. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-fibers；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,2,5]],"y_points":["a","b"],"q_map":["a","a","a","b","b","a"]}。請依 [fibers, surjective, fiber_cover, certificate] 欄序回答。

查看答案與解釋([[a, [0, 1, 2, 5]], [b, [3, 4]]], 是, 是, fibers_partition_X)

Wave6第十一層核對=([[a, [0, 1, 2, 5]], [b, [3, 4]]], 是, 是, fibers_partition_X)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0019/)

商拓撲 · qf-mod48-quotient-fibers · candidate





## 20. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-fibers；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,3,5]],"y_points":["a","b"],"q_map":["a","b","b","a","b","a"]}。請依 [fibers, surjective, fiber_cover, certificate] 欄序回答。

查看答案與解釋([[a, [0, 3, 5]], [b, [1, 2, 4]]], 是, 是, fibers_partition_X)

Wave6第十一層核對=([[a, [0, 3, 5]], [b, [1, 2, 4]]], 是, 是, fibers_partition_X)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0020/)

商拓撲 · qf-mod48-quotient-fibers · candidate





## 21. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-fibers；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,3,5]],"y_points":["a","b"],"q_map":["a","a","b","a","b","a"]}。請依 [fibers, surjective, fiber_cover, certificate] 欄序回答。

查看答案與解釋([[a, [0, 1, 3, 5]], [b, [2, 4]]], 是, 是, fibers_partition_X)

Wave6第十一層核對=([[a, [0, 1, 3, 5]], [b, [2, 4]]], 是, 是, fibers_partition_X)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0021/)

商拓撲 · qf-mod48-quotient-fibers · candidate





## 22. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-fibers；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,2,3,5]],"y_points":["a","b"],"q_map":["a","b","a","a","b","a"]}。請依 [fibers, surjective, fiber_cover, certificate] 欄序回答。

查看答案與解釋([[a, [0, 2, 3, 5]], [b, [1, 4]]], 是, 是, fibers_partition_X)

Wave6第十一層核對=([[a, [0, 2, 3, 5]], [b, [1, 4]]], 是, 是, fibers_partition_X)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0022/)

商拓撲 · qf-mod48-quotient-fibers · candidate





## 23. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-fibers；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,2,3,5]],"y_points":["a","b"],"q_map":["a","a","a","a","b","a"]}。請依 [fibers, surjective, fiber_cover, certificate] 欄序回答。

查看答案與解釋([[a, [0, 1, 2, 3, 5]], [b, [4]]], 是, 是, fibers_partition_X)

Wave6第十一層核對=([[a, [0, 1, 2, 3, 5]], [b, [4]]], 是, 是, fibers_partition_X)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0023/)

商拓撲 · qf-mod48-quotient-fibers · candidate





## 24. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-fibers；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,4,5]],"y_points":["a","b"],"q_map":["a","b","b","b","a","a"]}。請依 [fibers, surjective, fiber_cover, certificate] 欄序回答。

查看答案與解釋([[a, [0, 4, 5]], [b, [1, 2, 3]]], 是, 是, fibers_partition_X)

Wave6第十一層核對=([[a, [0, 4, 5]], [b, [1, 2, 3]]], 是, 是, fibers_partition_X)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0024/)

商拓撲 · qf-mod48-quotient-fibers · candidate





## 25. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-fibers；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,4,5]],"y_points":["a","b"],"q_map":["a","a","b","b","a","a"]}。請依 [fibers, surjective, fiber_cover, certificate] 欄序回答。

查看答案與解釋([[a, [0, 1, 4, 5]], [b, [2, 3]]], 是, 是, fibers_partition_X)

Wave6第十一層核對=([[a, [0, 1, 4, 5]], [b, [2, 3]]], 是, 是, fibers_partition_X)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0025/)

商拓撲 · qf-mod48-quotient-fibers · candidate





## 26. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-generation；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1]],"y_points":["a","b"],"q_map":["a","a","b","b","b","b"]}。請依 [fibers, final_topology, saturated_source_opens, open_count_correspondence, quotient_certificate, certificate] 欄序回答。

查看答案與解釋([[a, [0, 1]], [b, [2, 3, 4, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 1]], 是, 是, U_open_iff_q_preimage_U_open)

Wave6第十一層核對=([[a, [0, 1]], [b, [2, 3, 4, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 1]], 是, 是, U_open_iff_q_preimage_U_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0026/)

商拓撲 · qf-mod48-quotient-topology-generation · candidate





## 27. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-generation；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,2]],"y_points":["a","b"],"q_map":["a","b","a","b","b","b"]}。請依 [fibers, final_topology, saturated_source_opens, open_count_correspondence, quotient_certificate, certificate] 欄序回答。

查看答案與解釋([[a, [0, 2]], [b, [1, 3, 4, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 2]], 是, 是, U_open_iff_q_preimage_U_open)

Wave6第十一層核對=([[a, [0, 2]], [b, [1, 3, 4, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 2]], 是, 是, U_open_iff_q_preimage_U_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0027/)

商拓撲 · qf-mod48-quotient-topology-generation · candidate





## 28. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-generation；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,2]],"y_points":["a","b"],"q_map":["a","a","a","b","b","b"]}。請依 [fibers, final_topology, saturated_source_opens, open_count_correspondence, quotient_certificate, certificate] 欄序回答。

查看答案與解釋([[a, [0, 1, 2]], [b, [3, 4, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 1, 2]], 是, 是, U_open_iff_q_preimage_U_open)

Wave6第十一層核對=([[a, [0, 1, 2]], [b, [3, 4, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 1, 2]], 是, 是, U_open_iff_q_preimage_U_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0028/)

商拓撲 · qf-mod48-quotient-topology-generation · candidate





## 29. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-generation；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,3]],"y_points":["a","b"],"q_map":["a","b","b","a","b","b"]}。請依 [fibers, final_topology, saturated_source_opens, open_count_correspondence, quotient_certificate, certificate] 欄序回答。

查看答案與解釋([[a, [0, 3]], [b, [1, 2, 4, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 3]], 是, 是, U_open_iff_q_preimage_U_open)

Wave6第十一層核對=([[a, [0, 3]], [b, [1, 2, 4, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 3]], 是, 是, U_open_iff_q_preimage_U_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0029/)

商拓撲 · qf-mod48-quotient-topology-generation · candidate





## 30. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-generation；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,3]],"y_points":["a","b"],"q_map":["a","a","b","a","b","b"]}。請依 [fibers, final_topology, saturated_source_opens, open_count_correspondence, quotient_certificate, certificate] 欄序回答。

查看答案與解釋([[a, [0, 1, 3]], [b, [2, 4, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 1, 3]], 是, 是, U_open_iff_q_preimage_U_open)

Wave6第十一層核對=([[a, [0, 1, 3]], [b, [2, 4, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 1, 3]], 是, 是, U_open_iff_q_preimage_U_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0030/)

商拓撲 · qf-mod48-quotient-topology-generation · candidate





## 31. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-generation；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,2,3]],"y_points":["a","b"],"q_map":["a","b","a","a","b","b"]}。請依 [fibers, final_topology, saturated_source_opens, open_count_correspondence, quotient_certificate, certificate] 欄序回答。

查看答案與解釋([[a, [0, 2, 3]], [b, [1, 4, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 2, 3]], 是, 是, U_open_iff_q_preimage_U_open)

Wave6第十一層核對=([[a, [0, 2, 3]], [b, [1, 4, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 2, 3]], 是, 是, U_open_iff_q_preimage_U_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0031/)

商拓撲 · qf-mod48-quotient-topology-generation · candidate





## 32. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-generation；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,2,3]],"y_points":["a","b"],"q_map":["a","a","a","a","b","b"]}。請依 [fibers, final_topology, saturated_source_opens, open_count_correspondence, quotient_certificate, certificate] 欄序回答。

查看答案與解釋([[a, [0, 1, 2, 3]], [b, [4, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 1, 2, 3]], 是, 是, U_open_iff_q_preimage_U_open)

Wave6第十一層核對=([[a, [0, 1, 2, 3]], [b, [4, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 1, 2, 3]], 是, 是, U_open_iff_q_preimage_U_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0032/)

商拓撲 · qf-mod48-quotient-topology-generation · candidate





## 33. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-generation；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,4]],"y_points":["a","b"],"q_map":["a","b","b","b","a","b"]}。請依 [fibers, final_topology, saturated_source_opens, open_count_correspondence, quotient_certificate, certificate] 欄序回答。

查看答案與解釋([[a, [0, 4]], [b, [1, 2, 3, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 4]], 是, 是, U_open_iff_q_preimage_U_open)

Wave6第十一層核對=([[a, [0, 4]], [b, [1, 2, 3, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 4]], 是, 是, U_open_iff_q_preimage_U_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0033/)

商拓撲 · qf-mod48-quotient-topology-generation · candidate





## 34. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-generation；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,4]],"y_points":["a","b"],"q_map":["a","a","b","b","a","b"]}。請依 [fibers, final_topology, saturated_source_opens, open_count_correspondence, quotient_certificate, certificate] 欄序回答。

查看答案與解釋([[a, [0, 1, 4]], [b, [2, 3, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 1, 4]], 是, 是, U_open_iff_q_preimage_U_open)

Wave6第十一層核對=([[a, [0, 1, 4]], [b, [2, 3, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 1, 4]], 是, 是, U_open_iff_q_preimage_U_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0034/)

商拓撲 · qf-mod48-quotient-topology-generation · candidate





## 35. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-generation；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,2,4]],"y_points":["a","b"],"q_map":["a","b","a","b","a","b"]}。請依 [fibers, final_topology, saturated_source_opens, open_count_correspondence, quotient_certificate, certificate] 欄序回答。

查看答案與解釋([[a, [0, 2, 4]], [b, [1, 3, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 2, 4]], 是, 是, U_open_iff_q_preimage_U_open)

Wave6第十一層核對=([[a, [0, 2, 4]], [b, [1, 3, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 2, 4]], 是, 是, U_open_iff_q_preimage_U_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0035/)

商拓撲 · qf-mod48-quotient-topology-generation · candidate





## 36. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-generation；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,2,4]],"y_points":["a","b"],"q_map":["a","a","a","b","a","b"]}。請依 [fibers, final_topology, saturated_source_opens, open_count_correspondence, quotient_certificate, certificate] 欄序回答。

查看答案與解釋([[a, [0, 1, 2, 4]], [b, [3, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 1, 2, 4]], 是, 是, U_open_iff_q_preimage_U_open)

Wave6第十一層核對=([[a, [0, 1, 2, 4]], [b, [3, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 1, 2, 4]], 是, 是, U_open_iff_q_preimage_U_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0036/)

商拓撲 · qf-mod48-quotient-topology-generation · candidate





## 37. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-generation；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,3,4]],"y_points":["a","b"],"q_map":["a","b","b","a","a","b"]}。請依 [fibers, final_topology, saturated_source_opens, open_count_correspondence, quotient_certificate, certificate] 欄序回答。

查看答案與解釋([[a, [0, 3, 4]], [b, [1, 2, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 3, 4]], 是, 是, U_open_iff_q_preimage_U_open)

Wave6第十一層核對=([[a, [0, 3, 4]], [b, [1, 2, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 3, 4]], 是, 是, U_open_iff_q_preimage_U_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0037/)

商拓撲 · qf-mod48-quotient-topology-generation · candidate





## 38. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-generation；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,3,4]],"y_points":["a","b"],"q_map":["a","a","b","a","a","b"]}。請依 [fibers, final_topology, saturated_source_opens, open_count_correspondence, quotient_certificate, certificate] 欄序回答。

查看答案與解釋([[a, [0, 1, 3, 4]], [b, [2, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 1, 3, 4]], 是, 是, U_open_iff_q_preimage_U_open)

Wave6第十一層核對=([[a, [0, 1, 3, 4]], [b, [2, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 1, 3, 4]], 是, 是, U_open_iff_q_preimage_U_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0038/)

商拓撲 · qf-mod48-quotient-topology-generation · candidate





## 39. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-generation；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,2,3,4]],"y_points":["a","b"],"q_map":["a","b","a","a","a","b"]}。請依 [fibers, final_topology, saturated_source_opens, open_count_correspondence, quotient_certificate, certificate] 欄序回答。

查看答案與解釋([[a, [0, 2, 3, 4]], [b, [1, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 2, 3, 4]], 是, 是, U_open_iff_q_preimage_U_open)

Wave6第十一層核對=([[a, [0, 2, 3, 4]], [b, [1, 5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 2, 3, 4]], 是, 是, U_open_iff_q_preimage_U_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0039/)

商拓撲 · qf-mod48-quotient-topology-generation · candidate





## 40. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-generation；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,2,3,4]],"y_points":["a","b"],"q_map":["a","a","a","a","a","b"]}。請依 [fibers, final_topology, saturated_source_opens, open_count_correspondence, quotient_certificate, certificate] 欄序回答。

查看答案與解釋([[a, [0, 1, 2, 3, 4]], [b, [5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4]], 是, 是, U_open_iff_q_preimage_U_open)

Wave6第十一層核對=([[a, [0, 1, 2, 3, 4]], [b, [5]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4]], 是, 是, U_open_iff_q_preimage_U_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0040/)

商拓撲 · qf-mod48-quotient-topology-generation · candidate





## 41. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-generation；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,5]],"y_points":["a","b"],"q_map":["a","b","b","b","b","a"]}。請依 [fibers, final_topology, saturated_source_opens, open_count_correspondence, quotient_certificate, certificate] 欄序回答。

查看答案與解釋([[a, [0, 5]], [b, [1, 2, 3, 4]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 5]], 是, 是, U_open_iff_q_preimage_U_open)

Wave6第十一層核對=([[a, [0, 5]], [b, [1, 2, 3, 4]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 5]], 是, 是, U_open_iff_q_preimage_U_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0041/)

商拓撲 · qf-mod48-quotient-topology-generation · candidate





## 42. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-generation；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,5]],"y_points":["a","b"],"q_map":["a","a","b","b","b","a"]}。請依 [fibers, final_topology, saturated_source_opens, open_count_correspondence, quotient_certificate, certificate] 欄序回答。

查看答案與解釋([[a, [0, 1, 5]], [b, [2, 3, 4]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 1, 5]], 是, 是, U_open_iff_q_preimage_U_open)

Wave6第十一層核對=([[a, [0, 1, 5]], [b, [2, 3, 4]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 1, 5]], 是, 是, U_open_iff_q_preimage_U_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0042/)

商拓撲 · qf-mod48-quotient-topology-generation · candidate





## 43. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-generation；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,2,5]],"y_points":["a","b"],"q_map":["a","b","a","b","b","a"]}。請依 [fibers, final_topology, saturated_source_opens, open_count_correspondence, quotient_certificate, certificate] 欄序回答。

查看答案與解釋([[a, [0, 2, 5]], [b, [1, 3, 4]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 2, 5]], 是, 是, U_open_iff_q_preimage_U_open)

Wave6第十一層核對=([[a, [0, 2, 5]], [b, [1, 3, 4]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 2, 5]], 是, 是, U_open_iff_q_preimage_U_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0043/)

商拓撲 · qf-mod48-quotient-topology-generation · candidate





## 44. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-generation；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,2,5]],"y_points":["a","b"],"q_map":["a","a","a","b","b","a"]}。請依 [fibers, final_topology, saturated_source_opens, open_count_correspondence, quotient_certificate, certificate] 欄序回答。

查看答案與解釋([[a, [0, 1, 2, 5]], [b, [3, 4]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 1, 2, 5]], 是, 是, U_open_iff_q_preimage_U_open)

Wave6第十一層核對=([[a, [0, 1, 2, 5]], [b, [3, 4]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 1, 2, 5]], 是, 是, U_open_iff_q_preimage_U_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0044/)

商拓撲 · qf-mod48-quotient-topology-generation · candidate





## 45. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-generation；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,3,5]],"y_points":["a","b"],"q_map":["a","b","b","a","b","a"]}。請依 [fibers, final_topology, saturated_source_opens, open_count_correspondence, quotient_certificate, certificate] 欄序回答。

查看答案與解釋([[a, [0, 3, 5]], [b, [1, 2, 4]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 3, 5]], 是, 是, U_open_iff_q_preimage_U_open)

Wave6第十一層核對=([[a, [0, 3, 5]], [b, [1, 2, 4]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 3, 5]], 是, 是, U_open_iff_q_preimage_U_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0045/)

商拓撲 · qf-mod48-quotient-topology-generation · candidate





## 46. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-generation；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,3,5]],"y_points":["a","b"],"q_map":["a","a","b","a","b","a"]}。請依 [fibers, final_topology, saturated_source_opens, open_count_correspondence, quotient_certificate, certificate] 欄序回答。

查看答案與解釋([[a, [0, 1, 3, 5]], [b, [2, 4]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 1, 3, 5]], 是, 是, U_open_iff_q_preimage_U_open)

Wave6第十一層核對=([[a, [0, 1, 3, 5]], [b, [2, 4]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 1, 3, 5]], 是, 是, U_open_iff_q_preimage_U_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0046/)

商拓撲 · qf-mod48-quotient-topology-generation · candidate





## 47. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-generation；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,2,3,5]],"y_points":["a","b"],"q_map":["a","b","a","a","b","a"]}。請依 [fibers, final_topology, saturated_source_opens, open_count_correspondence, quotient_certificate, certificate] 欄序回答。

查看答案與解釋([[a, [0, 2, 3, 5]], [b, [1, 4]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 2, 3, 5]], 是, 是, U_open_iff_q_preimage_U_open)

Wave6第十一層核對=([[a, [0, 2, 3, 5]], [b, [1, 4]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 2, 3, 5]], 是, 是, U_open_iff_q_preimage_U_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0047/)

商拓撲 · qf-mod48-quotient-topology-generation · candidate





## 48. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-generation；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,2,3,5]],"y_points":["a","b"],"q_map":["a","a","a","a","b","a"]}。請依 [fibers, final_topology, saturated_source_opens, open_count_correspondence, quotient_certificate, certificate] 欄序回答。

查看答案與解釋([[a, [0, 1, 2, 3, 5]], [b, [4]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 5]], 是, 是, U_open_iff_q_preimage_U_open)

Wave6第十一層核對=([[a, [0, 1, 2, 3, 5]], [b, [4]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 5]], 是, 是, U_open_iff_q_preimage_U_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0048/)

商拓撲 · qf-mod48-quotient-topology-generation · candidate





## 49. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-generation；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,4,5]],"y_points":["a","b"],"q_map":["a","b","b","b","a","a"]}。請依 [fibers, final_topology, saturated_source_opens, open_count_correspondence, quotient_certificate, certificate] 欄序回答。

查看答案與解釋([[a, [0, 4, 5]], [b, [1, 2, 3]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 4, 5]], 是, 是, U_open_iff_q_preimage_U_open)

Wave6第十一層核對=([[a, [0, 4, 5]], [b, [1, 2, 3]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 4, 5]], 是, 是, U_open_iff_q_preimage_U_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0049/)

商拓撲 · qf-mod48-quotient-topology-generation · candidate





## 50. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-generation；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,4,5]],"y_points":["a","b"],"q_map":["a","a","b","b","a","a"]}。請依 [fibers, final_topology, saturated_source_opens, open_count_correspondence, quotient_certificate, certificate] 欄序回答。

查看答案與解釋([[a, [0, 1, 4, 5]], [b, [2, 3]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 1, 4, 5]], 是, 是, U_open_iff_q_preimage_U_open)

Wave6第十一層核對=([[a, [0, 1, 4, 5]], [b, [2, 3]]], [[a, b], [a], []], [[], [0, 1, 2, 3, 4, 5], [0, 1, 4, 5]], 是, 是, U_open_iff_q_preimage_U_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0050/)

商拓撲 · qf-mod48-quotient-topology-generation · candidate





## 51. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-final-continuity；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1]],"y_points":["a","b"],"q_map":["a","a","b","b","b","b"],"z_points":[0,1],"z_topology":[[],[1],[0,1]],"h_map":[0,1]}。請依 [h_continuous, composite_continuous, criterion_equivalence, h_rows, composite_rows, certificate] 欄序回答。

h與h∘q可同為不連續而criterion_equivalence為是；此等價需本節已認證的surjection與final topology。

查看答案與解釋(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 0], [2, 1], [3, 1], [4, 1], [5, 1]], quotient_final_property_for_surjective_q)

Wave6第十一層核對=(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 0], [2, 1], [3, 1], [4, 1], [5, 1]], quotient_final_property_for_surjective_q)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0051/)

商拓撲 · qf-mod48-quotient-final-continuity · candidate





## 52. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-final-continuity；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,2]],"y_points":["a","b"],"q_map":["a","b","a","b","b","b"],"z_points":[0,1],"z_topology":[[],[1],[0,1]],"h_map":[0,1]}。請依 [h_continuous, composite_continuous, criterion_equivalence, h_rows, composite_rows, certificate] 欄序回答。

h與h∘q可同為不連續而criterion_equivalence為是；此等價需本節已認證的surjection與final topology。

查看答案與解釋(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 0], [3, 1], [4, 1], [5, 1]], quotient_final_property_for_surjective_q)

Wave6第十一層核對=(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 0], [3, 1], [4, 1], [5, 1]], quotient_final_property_for_surjective_q)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0052/)

商拓撲 · qf-mod48-quotient-final-continuity · candidate





## 53. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-final-continuity；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,2]],"y_points":["a","b"],"q_map":["a","a","a","b","b","b"],"z_points":[0,1],"z_topology":[[],[1],[0,1]],"h_map":[0,1]}。請依 [h_continuous, composite_continuous, criterion_equivalence, h_rows, composite_rows, certificate] 欄序回答。

h與h∘q可同為不連續而criterion_equivalence為是；此等價需本節已認證的surjection與final topology。

查看答案與解釋(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 0], [2, 0], [3, 1], [4, 1], [5, 1]], quotient_final_property_for_surjective_q)

Wave6第十一層核對=(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 0], [2, 0], [3, 1], [4, 1], [5, 1]], quotient_final_property_for_surjective_q)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0053/)

商拓撲 · qf-mod48-quotient-final-continuity · candidate





## 54. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-final-continuity；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,3]],"y_points":["a","b"],"q_map":["a","b","b","a","b","b"],"z_points":[0,1],"z_topology":[[],[1],[0,1]],"h_map":[0,1]}。請依 [h_continuous, composite_continuous, criterion_equivalence, h_rows, composite_rows, certificate] 欄序回答。

h與h∘q可同為不連續而criterion_equivalence為是；此等價需本節已認證的surjection與final topology。

查看答案與解釋(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 1], [3, 0], [4, 1], [5, 1]], quotient_final_property_for_surjective_q)

Wave6第十一層核對=(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 1], [3, 0], [4, 1], [5, 1]], quotient_final_property_for_surjective_q)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0054/)

商拓撲 · qf-mod48-quotient-final-continuity · candidate





## 55. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-final-continuity；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,3]],"y_points":["a","b"],"q_map":["a","a","b","a","b","b"],"z_points":[0,1],"z_topology":[[],[1],[0,1]],"h_map":[0,1]}。請依 [h_continuous, composite_continuous, criterion_equivalence, h_rows, composite_rows, certificate] 欄序回答。

h與h∘q可同為不連續而criterion_equivalence為是；此等價需本節已認證的surjection與final topology。

查看答案與解釋(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 0], [2, 1], [3, 0], [4, 1], [5, 1]], quotient_final_property_for_surjective_q)

Wave6第十一層核對=(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 0], [2, 1], [3, 0], [4, 1], [5, 1]], quotient_final_property_for_surjective_q)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0055/)

商拓撲 · qf-mod48-quotient-final-continuity · candidate





## 56. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-final-continuity；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,2,3]],"y_points":["a","b"],"q_map":["a","b","a","a","b","b"],"z_points":[0,1],"z_topology":[[],[1],[0,1]],"h_map":[0,1]}。請依 [h_continuous, composite_continuous, criterion_equivalence, h_rows, composite_rows, certificate] 欄序回答。

h與h∘q可同為不連續而criterion_equivalence為是；此等價需本節已認證的surjection與final topology。

查看答案與解釋(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 0], [3, 0], [4, 1], [5, 1]], quotient_final_property_for_surjective_q)

Wave6第十一層核對=(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 0], [3, 0], [4, 1], [5, 1]], quotient_final_property_for_surjective_q)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0056/)

商拓撲 · qf-mod48-quotient-final-continuity · candidate





## 57. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-final-continuity；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,2,3]],"y_points":["a","b"],"q_map":["a","a","a","a","b","b"],"z_points":[0,1],"z_topology":[[],[1],[0,1]],"h_map":[0,1]}。請依 [h_continuous, composite_continuous, criterion_equivalence, h_rows, composite_rows, certificate] 欄序回答。

h與h∘q可同為不連續而criterion_equivalence為是；此等價需本節已認證的surjection與final topology。

查看答案與解釋(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 0], [2, 0], [3, 0], [4, 1], [5, 1]], quotient_final_property_for_surjective_q)

Wave6第十一層核對=(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 0], [2, 0], [3, 0], [4, 1], [5, 1]], quotient_final_property_for_surjective_q)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0057/)

商拓撲 · qf-mod48-quotient-final-continuity · candidate





## 58. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-final-continuity；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,4]],"y_points":["a","b"],"q_map":["a","b","b","b","a","b"],"z_points":[0,1],"z_topology":[[],[1],[0,1]],"h_map":[0,1]}。請依 [h_continuous, composite_continuous, criterion_equivalence, h_rows, composite_rows, certificate] 欄序回答。

h與h∘q可同為不連續而criterion_equivalence為是；此等價需本節已認證的surjection與final topology。

查看答案與解釋(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 1], [3, 1], [4, 0], [5, 1]], quotient_final_property_for_surjective_q)

Wave6第十一層核對=(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 1], [3, 1], [4, 0], [5, 1]], quotient_final_property_for_surjective_q)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0058/)

商拓撲 · qf-mod48-quotient-final-continuity · candidate





## 59. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-final-continuity；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,4]],"y_points":["a","b"],"q_map":["a","a","b","b","a","b"],"z_points":[0,1],"z_topology":[[],[1],[0,1]],"h_map":[0,1]}。請依 [h_continuous, composite_continuous, criterion_equivalence, h_rows, composite_rows, certificate] 欄序回答。

h與h∘q可同為不連續而criterion_equivalence為是；此等價需本節已認證的surjection與final topology。

查看答案與解釋(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 0], [2, 1], [3, 1], [4, 0], [5, 1]], quotient_final_property_for_surjective_q)

Wave6第十一層核對=(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 0], [2, 1], [3, 1], [4, 0], [5, 1]], quotient_final_property_for_surjective_q)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0059/)

商拓撲 · qf-mod48-quotient-final-continuity · candidate





## 60. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-final-continuity；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,2,4]],"y_points":["a","b"],"q_map":["a","b","a","b","a","b"],"z_points":[0,1],"z_topology":[[],[1],[0,1]],"h_map":[0,1]}。請依 [h_continuous, composite_continuous, criterion_equivalence, h_rows, composite_rows, certificate] 欄序回答。

h與h∘q可同為不連續而criterion_equivalence為是；此等價需本節已認證的surjection與final topology。

查看答案與解釋(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 0], [3, 1], [4, 0], [5, 1]], quotient_final_property_for_surjective_q)

Wave6第十一層核對=(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 0], [3, 1], [4, 0], [5, 1]], quotient_final_property_for_surjective_q)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0060/)

商拓撲 · qf-mod48-quotient-final-continuity · candidate





## 61. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-final-continuity；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,2,4]],"y_points":["a","b"],"q_map":["a","a","a","b","a","b"],"z_points":[0,1],"z_topology":[[],[1],[0,1]],"h_map":[0,1]}。請依 [h_continuous, composite_continuous, criterion_equivalence, h_rows, composite_rows, certificate] 欄序回答。

h與h∘q可同為不連續而criterion_equivalence為是；此等價需本節已認證的surjection與final topology。

查看答案與解釋(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 0], [2, 0], [3, 1], [4, 0], [5, 1]], quotient_final_property_for_surjective_q)

Wave6第十一層核對=(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 0], [2, 0], [3, 1], [4, 0], [5, 1]], quotient_final_property_for_surjective_q)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0061/)

商拓撲 · qf-mod48-quotient-final-continuity · candidate





## 62. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-final-continuity；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,3,4]],"y_points":["a","b"],"q_map":["a","b","b","a","a","b"],"z_points":[0,1],"z_topology":[[],[1],[0,1]],"h_map":[0,1]}。請依 [h_continuous, composite_continuous, criterion_equivalence, h_rows, composite_rows, certificate] 欄序回答。

h與h∘q可同為不連續而criterion_equivalence為是；此等價需本節已認證的surjection與final topology。

查看答案與解釋(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 1], [3, 0], [4, 0], [5, 1]], quotient_final_property_for_surjective_q)

Wave6第十一層核對=(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 1], [3, 0], [4, 0], [5, 1]], quotient_final_property_for_surjective_q)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0062/)

商拓撲 · qf-mod48-quotient-final-continuity · candidate





## 63. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-final-continuity；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,3,4]],"y_points":["a","b"],"q_map":["a","a","b","a","a","b"],"z_points":[0,1],"z_topology":[[],[1],[0,1]],"h_map":[0,1]}。請依 [h_continuous, composite_continuous, criterion_equivalence, h_rows, composite_rows, certificate] 欄序回答。

h與h∘q可同為不連續而criterion_equivalence為是；此等價需本節已認證的surjection與final topology。

查看答案與解釋(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 0], [2, 1], [3, 0], [4, 0], [5, 1]], quotient_final_property_for_surjective_q)

Wave6第十一層核對=(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 0], [2, 1], [3, 0], [4, 0], [5, 1]], quotient_final_property_for_surjective_q)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0063/)

商拓撲 · qf-mod48-quotient-final-continuity · candidate





## 64. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-final-continuity；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,2,3,4]],"y_points":["a","b"],"q_map":["a","b","a","a","a","b"],"z_points":[0,1],"z_topology":[[],[1],[0,1]],"h_map":[0,1]}。請依 [h_continuous, composite_continuous, criterion_equivalence, h_rows, composite_rows, certificate] 欄序回答。

h與h∘q可同為不連續而criterion_equivalence為是；此等價需本節已認證的surjection與final topology。

查看答案與解釋(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 0], [3, 0], [4, 0], [5, 1]], quotient_final_property_for_surjective_q)

Wave6第十一層核對=(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 0], [3, 0], [4, 0], [5, 1]], quotient_final_property_for_surjective_q)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0064/)

商拓撲 · qf-mod48-quotient-final-continuity · candidate





## 65. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-final-continuity；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,2,3,4]],"y_points":["a","b"],"q_map":["a","a","a","a","a","b"],"z_points":[0,1],"z_topology":[[],[1],[0,1]],"h_map":[0,1]}。請依 [h_continuous, composite_continuous, criterion_equivalence, h_rows, composite_rows, certificate] 欄序回答。

h與h∘q可同為不連續而criterion_equivalence為是；此等價需本節已認證的surjection與final topology。

查看答案與解釋(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 0], [2, 0], [3, 0], [4, 0], [5, 1]], quotient_final_property_for_surjective_q)

Wave6第十一層核對=(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 0], [2, 0], [3, 0], [4, 0], [5, 1]], quotient_final_property_for_surjective_q)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0065/)

商拓撲 · qf-mod48-quotient-final-continuity · candidate





## 66. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-final-continuity；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,5]],"y_points":["a","b"],"q_map":["a","b","b","b","b","a"],"z_points":[0,1],"z_topology":[[],[1],[0,1]],"h_map":[0,1]}。請依 [h_continuous, composite_continuous, criterion_equivalence, h_rows, composite_rows, certificate] 欄序回答。

h與h∘q可同為不連續而criterion_equivalence為是；此等價需本節已認證的surjection與final topology。

查看答案與解釋(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 1], [3, 1], [4, 1], [5, 0]], quotient_final_property_for_surjective_q)

Wave6第十一層核對=(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 1], [3, 1], [4, 1], [5, 0]], quotient_final_property_for_surjective_q)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0066/)

商拓撲 · qf-mod48-quotient-final-continuity · candidate





## 67. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-final-continuity；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,5]],"y_points":["a","b"],"q_map":["a","a","b","b","b","a"],"z_points":[0,1],"z_topology":[[],[1],[0,1]],"h_map":[0,1]}。請依 [h_continuous, composite_continuous, criterion_equivalence, h_rows, composite_rows, certificate] 欄序回答。

h與h∘q可同為不連續而criterion_equivalence為是；此等價需本節已認證的surjection與final topology。

查看答案與解釋(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 0], [2, 1], [3, 1], [4, 1], [5, 0]], quotient_final_property_for_surjective_q)

Wave6第十一層核對=(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 0], [2, 1], [3, 1], [4, 1], [5, 0]], quotient_final_property_for_surjective_q)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0067/)

商拓撲 · qf-mod48-quotient-final-continuity · candidate





## 68. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-final-continuity；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,2,5]],"y_points":["a","b"],"q_map":["a","b","a","b","b","a"],"z_points":[0,1],"z_topology":[[],[1],[0,1]],"h_map":[0,1]}。請依 [h_continuous, composite_continuous, criterion_equivalence, h_rows, composite_rows, certificate] 欄序回答。

h與h∘q可同為不連續而criterion_equivalence為是；此等價需本節已認證的surjection與final topology。

查看答案與解釋(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 0], [3, 1], [4, 1], [5, 0]], quotient_final_property_for_surjective_q)

Wave6第十一層核對=(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 0], [3, 1], [4, 1], [5, 0]], quotient_final_property_for_surjective_q)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0068/)

商拓撲 · qf-mod48-quotient-final-continuity · candidate





## 69. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-final-continuity；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,2,5]],"y_points":["a","b"],"q_map":["a","a","a","b","b","a"],"z_points":[0,1],"z_topology":[[],[1],[0,1]],"h_map":[0,1]}。請依 [h_continuous, composite_continuous, criterion_equivalence, h_rows, composite_rows, certificate] 欄序回答。

h與h∘q可同為不連續而criterion_equivalence為是；此等價需本節已認證的surjection與final topology。

查看答案與解釋(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 0], [2, 0], [3, 1], [4, 1], [5, 0]], quotient_final_property_for_surjective_q)

Wave6第十一層核對=(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 0], [2, 0], [3, 1], [4, 1], [5, 0]], quotient_final_property_for_surjective_q)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0069/)

商拓撲 · qf-mod48-quotient-final-continuity · candidate





## 70. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-final-continuity；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,3,5]],"y_points":["a","b"],"q_map":["a","b","b","a","b","a"],"z_points":[0,1],"z_topology":[[],[1],[0,1]],"h_map":[0,1]}。請依 [h_continuous, composite_continuous, criterion_equivalence, h_rows, composite_rows, certificate] 欄序回答。

h與h∘q可同為不連續而criterion_equivalence為是；此等價需本節已認證的surjection與final topology。

查看答案與解釋(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 1], [3, 0], [4, 1], [5, 0]], quotient_final_property_for_surjective_q)

Wave6第十一層核對=(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 1], [3, 0], [4, 1], [5, 0]], quotient_final_property_for_surjective_q)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0070/)

商拓撲 · qf-mod48-quotient-final-continuity · candidate





## 71. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-final-continuity；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,3,5]],"y_points":["a","b"],"q_map":["a","a","b","a","b","a"],"z_points":[0,1],"z_topology":[[],[1],[0,1]],"h_map":[0,1]}。請依 [h_continuous, composite_continuous, criterion_equivalence, h_rows, composite_rows, certificate] 欄序回答。

h與h∘q可同為不連續而criterion_equivalence為是；此等價需本節已認證的surjection與final topology。

查看答案與解釋(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 0], [2, 1], [3, 0], [4, 1], [5, 0]], quotient_final_property_for_surjective_q)

Wave6第十一層核對=(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 0], [2, 1], [3, 0], [4, 1], [5, 0]], quotient_final_property_for_surjective_q)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0071/)

商拓撲 · qf-mod48-quotient-final-continuity · candidate





## 72. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-final-continuity；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,2,3,5]],"y_points":["a","b"],"q_map":["a","b","a","a","b","a"],"z_points":[0,1],"z_topology":[[],[1],[0,1]],"h_map":[0,1]}。請依 [h_continuous, composite_continuous, criterion_equivalence, h_rows, composite_rows, certificate] 欄序回答。

h與h∘q可同為不連續而criterion_equivalence為是；此等價需本節已認證的surjection與final topology。

查看答案與解釋(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 0], [3, 0], [4, 1], [5, 0]], quotient_final_property_for_surjective_q)

Wave6第十一層核對=(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 0], [3, 0], [4, 1], [5, 0]], quotient_final_property_for_surjective_q)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0072/)

商拓撲 · qf-mod48-quotient-final-continuity · candidate





## 73. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-final-continuity；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,2,3,5]],"y_points":["a","b"],"q_map":["a","a","a","a","b","a"],"z_points":[0,1],"z_topology":[[],[1],[0,1]],"h_map":[0,1]}。請依 [h_continuous, composite_continuous, criterion_equivalence, h_rows, composite_rows, certificate] 欄序回答。

h與h∘q可同為不連續而criterion_equivalence為是；此等價需本節已認證的surjection與final topology。

查看答案與解釋(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 0], [2, 0], [3, 0], [4, 1], [5, 0]], quotient_final_property_for_surjective_q)

Wave6第十一層核對=(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 0], [2, 0], [3, 0], [4, 1], [5, 0]], quotient_final_property_for_surjective_q)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0073/)

商拓撲 · qf-mod48-quotient-final-continuity · candidate





## 74. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-final-continuity；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,4,5]],"y_points":["a","b"],"q_map":["a","b","b","b","a","a"],"z_points":[0,1],"z_topology":[[],[1],[0,1]],"h_map":[0,1]}。請依 [h_continuous, composite_continuous, criterion_equivalence, h_rows, composite_rows, certificate] 欄序回答。

h與h∘q可同為不連續而criterion_equivalence為是；此等價需本節已認證的surjection與final topology。

查看答案與解釋(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 1], [3, 1], [4, 0], [5, 0]], quotient_final_property_for_surjective_q)

Wave6第十一層核對=(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 1], [3, 1], [4, 0], [5, 0]], quotient_final_property_for_surjective_q)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0074/)

商拓撲 · qf-mod48-quotient-final-continuity · candidate





## 75. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-final-continuity；資料={"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,4,5]],"y_points":["a","b"],"q_map":["a","a","b","b","a","a"],"z_points":[0,1],"z_topology":[[],[1],[0,1]],"h_map":[0,1]}。請依 [h_continuous, composite_continuous, criterion_equivalence, h_rows, composite_rows, certificate] 欄序回答。

h與h∘q可同為不連續而criterion_equivalence為是；此等價需本節已認證的surjection與final topology。

查看答案與解釋(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 0], [2, 1], [3, 1], [4, 0], [5, 0]], quotient_final_property_for_surjective_q)

Wave6第十一層核對=(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 0], [2, 1], [3, 1], [4, 0], [5, 0]], quotient_final_property_for_surjective_q)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0075/)

商拓撲 · qf-mod48-quotient-final-continuity · candidate





## 76. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-boundary；資料={"mode":"non_surjective","model":{"x_points":[0,1,2,3],"x_topology":[[],[0],[0,1,2,3]],"y_points":["y0","y1","y2","y3","y4"],"q_map":["y0","y1","y2","y3"]}}。請依 [mode, fibers, surjective, final_topology, final_topology_exists, quotient_map_claim, boundary] 欄序回答。

四種mode為7/8/7/7欄。非滿射仍由逆像iff定義final topology，但依本節慣例不是quotient map；僅有continuity不足以唯一指定final topology。

查看答案與解釋(non_surjective, [[y0, [0]], [y1, [1]], [y2, [2]], [y3, [3]], [y4, []]], 否, [[y0, y1, y2, y3, y4], [y0, y1, y2, y3], [y0, y4], [y0], [y4], []], 是, 否, preimage_defined_final_topology_exists_but_map_is_not_a_quotient_map_by_this_convention)

Wave6第十一層核對=(non_surjective, [[y0, [0]], [y1, [1]], [y2, [2]], [y3, [3]], [y4, []]], 否, [[y0, y1, y2, y3, y4], [y0, y1, y2, y3], [y0, y4], [y0], [y4], []], 是, 否, preimage_defined_final_topology_exists_but_map_is_not_a_quotient_map_by_this_convention)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0076/)

商拓撲 · qf-mod48-quotient-topology-boundary · candidate





## 77. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-boundary；資料={"mode":"open_image_error","model":{"x_points":[0,1,2,3,4],"x_topology":[[],[0],[0,1,2,3,4]],"y_points":["a","b"],"q_map":["a","a","a","b","b"],"subset":[0]}}。請依 [mode, source_subset, source_open, image, image_preimage, image_open, automatic_open_map_claim, boundary] 欄序回答。

四種mode為7/8/7/7欄。非滿射仍由逆像iff定義final topology，但依本節慣例不是quotient map；僅有continuity不足以唯一指定final topology。

查看答案與解釋(open_image_error, [0], 是, [a], [0, 1, 2], 否, 否, quotient_maps_need_not_be_open)

Wave6第十一層核對=(open_image_error, [0], 是, [a], [0, 1, 2], 否, 否, quotient_maps_need_not_be_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0077/)

商拓撲 · qf-mod48-quotient-topology-boundary · candidate





## 78. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-boundary；資料={"mode":"coarser_target","model":{"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,2]],"y_points":["a","b"],"q_map":["a","a","a","b","b","b"],"candidate_topology":[[],["a","b"]]}}。請依 [mode, candidate_topology, final_topology, q_continuous, properly_coarser, final_topology_identification_claim, boundary] 欄序回答。

四種mode為7/8/7/7欄。非滿射仍由逆像iff定義final topology，但依本節慣例不是quotient map；僅有continuity不足以唯一指定final topology。

查看答案與解釋(coarser_target, [[a, b], []], [[a, b], [a], []], 是, 是, 否, continuity_alone_does_not_identify_the_final_topology)

Wave6第十一層核對=(coarser_target, [[a, b], []], [[a, b], [a], []], 是, 是, 否, continuity_alone_does_not_identify_the_final_topology)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0078/)

商拓撲 · qf-mod48-quotient-topology-boundary · candidate





## 79. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-boundary；資料={"mode":"fiber_split","model":{"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5]],"y_points":["a","b"],"q_map":["a","a","b","b","b","b"],"subset":[0]}}。請依 [mode, source_subset, image, saturation, saturated, full_preimage_claim, boundary] 欄序回答。

四種mode為7/8/7/7欄。非滿射仍由逆像iff定義final topology，但依本節慣例不是quotient map；僅有continuity不足以唯一指定final topology。

查看答案與解釋(fiber_split, [0], [a], [0, 1], 否, 否, only_saturated_subsets_are_full_preimages)

Wave6第十一層核對=(fiber_split, [0], [a], [0, 1], 否, 否, only_saturated_subsets_are_full_preimages)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0079/)

商拓撲 · qf-mod48-quotient-topology-boundary · candidate





## 80. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-boundary；資料={"mode":"non_surjective","model":{"x_points":[0,1,2,3],"x_topology":[[],[1],[0,1,2,3]],"y_points":["y0","y1","y2","y3","y4"],"q_map":["y0","y1","y2","y3"]}}。請依 [mode, fibers, surjective, final_topology, final_topology_exists, quotient_map_claim, boundary] 欄序回答。

四種mode為7/8/7/7欄。非滿射仍由逆像iff定義final topology，但依本節慣例不是quotient map；僅有continuity不足以唯一指定final topology。

查看答案與解釋(non_surjective, [[y0, [0]], [y1, [1]], [y2, [2]], [y3, [3]], [y4, []]], 否, [[y0, y1, y2, y3, y4], [y0, y1, y2, y3], [y1, y4], [y1], [y4], []], 是, 否, preimage_defined_final_topology_exists_but_map_is_not_a_quotient_map_by_this_convention)

Wave6第十一層核對=(non_surjective, [[y0, [0]], [y1, [1]], [y2, [2]], [y3, [3]], [y4, []]], 否, [[y0, y1, y2, y3, y4], [y0, y1, y2, y3], [y1, y4], [y1], [y4], []], 是, 否, preimage_defined_final_topology_exists_but_map_is_not_a_quotient_map_by_this_convention)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0080/)

商拓撲 · qf-mod48-quotient-topology-boundary · candidate





## 81. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-boundary；資料={"mode":"open_image_error","model":{"x_points":[0,1,2,3,4],"x_topology":[[],[1],[0,1,2,3,4]],"y_points":["a","b"],"q_map":["a","a","a","b","b"],"subset":[1]}}。請依 [mode, source_subset, source_open, image, image_preimage, image_open, automatic_open_map_claim, boundary] 欄序回答。

四種mode為7/8/7/7欄。非滿射仍由逆像iff定義final topology，但依本節慣例不是quotient map；僅有continuity不足以唯一指定final topology。

查看答案與解釋(open_image_error, [1], 是, [a], [0, 1, 2], 否, 否, quotient_maps_need_not_be_open)

Wave6第十一層核對=(open_image_error, [1], 是, [a], [0, 1, 2], 否, 否, quotient_maps_need_not_be_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0081/)

商拓撲 · qf-mod48-quotient-topology-boundary · candidate





## 82. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-boundary；資料={"mode":"coarser_target","model":{"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,2,3]],"y_points":["a","b"],"q_map":["a","a","a","a","b","b"],"candidate_topology":[[],["a","b"]]}}。請依 [mode, candidate_topology, final_topology, q_continuous, properly_coarser, final_topology_identification_claim, boundary] 欄序回答。

四種mode為7/8/7/7欄。非滿射仍由逆像iff定義final topology，但依本節慣例不是quotient map；僅有continuity不足以唯一指定final topology。

查看答案與解釋(coarser_target, [[a, b], []], [[a, b], [a], []], 是, 是, 否, continuity_alone_does_not_identify_the_final_topology)

Wave6第十一層核對=(coarser_target, [[a, b], []], [[a, b], [a], []], 是, 是, 否, continuity_alone_does_not_identify_the_final_topology)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0082/)

商拓撲 · qf-mod48-quotient-topology-boundary · candidate





## 83. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-boundary；資料={"mode":"fiber_split","model":{"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5]],"y_points":["a","b"],"q_map":["a","b","a","b","b","b"],"subset":[0]}}。請依 [mode, source_subset, image, saturation, saturated, full_preimage_claim, boundary] 欄序回答。

四種mode為7/8/7/7欄。非滿射仍由逆像iff定義final topology，但依本節慣例不是quotient map；僅有continuity不足以唯一指定final topology。

查看答案與解釋(fiber_split, [0], [a], [0, 2], 否, 否, only_saturated_subsets_are_full_preimages)

Wave6第十一層核對=(fiber_split, [0], [a], [0, 2], 否, 否, only_saturated_subsets_are_full_preimages)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0083/)

商拓撲 · qf-mod48-quotient-topology-boundary · candidate





## 84. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-boundary；資料={"mode":"non_surjective","model":{"x_points":[0,1,2,3],"x_topology":[[],[0,1],[0,1,2,3]],"y_points":["y0","y1","y2","y3","y4"],"q_map":["y0","y1","y2","y3"]}}。請依 [mode, fibers, surjective, final_topology, final_topology_exists, quotient_map_claim, boundary] 欄序回答。

四種mode為7/8/7/7欄。非滿射仍由逆像iff定義final topology，但依本節慣例不是quotient map；僅有continuity不足以唯一指定final topology。

查看答案與解釋(non_surjective, [[y0, [0]], [y1, [1]], [y2, [2]], [y3, [3]], [y4, []]], 否, [[y0, y1, y2, y3, y4], [y0, y1, y2, y3], [y0, y1, y4], [y0, y1], [y4], []], 是, 否, preimage_defined_final_topology_exists_but_map_is_not_a_quotient_map_by_this_convention)

Wave6第十一層核對=(non_surjective, [[y0, [0]], [y1, [1]], [y2, [2]], [y3, [3]], [y4, []]], 否, [[y0, y1, y2, y3, y4], [y0, y1, y2, y3], [y0, y1, y4], [y0, y1], [y4], []], 是, 否, preimage_defined_final_topology_exists_but_map_is_not_a_quotient_map_by_this_convention)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0084/)

商拓撲 · qf-mod48-quotient-topology-boundary · candidate





## 85. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-boundary；資料={"mode":"open_image_error","model":{"x_points":[0,1,2,3,4],"x_topology":[[],[0,1],[0,1,2,3,4]],"y_points":["a","b"],"q_map":["a","a","a","b","b"],"subset":[0,1]}}。請依 [mode, source_subset, source_open, image, image_preimage, image_open, automatic_open_map_claim, boundary] 欄序回答。

四種mode為7/8/7/7欄。非滿射仍由逆像iff定義final topology，但依本節慣例不是quotient map；僅有continuity不足以唯一指定final topology。

查看答案與解釋(open_image_error, [0, 1], 是, [a], [0, 1, 2], 否, 否, quotient_maps_need_not_be_open)

Wave6第十一層核對=(open_image_error, [0, 1], 是, [a], [0, 1, 2], 否, 否, quotient_maps_need_not_be_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0085/)

商拓撲 · qf-mod48-quotient-topology-boundary · candidate





## 86. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-boundary；資料={"mode":"coarser_target","model":{"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,2,4]],"y_points":["a","b"],"q_map":["a","a","a","b","a","b"],"candidate_topology":[[],["a","b"]]}}。請依 [mode, candidate_topology, final_topology, q_continuous, properly_coarser, final_topology_identification_claim, boundary] 欄序回答。

四種mode為7/8/7/7欄。非滿射仍由逆像iff定義final topology，但依本節慣例不是quotient map；僅有continuity不足以唯一指定final topology。

查看答案與解釋(coarser_target, [[a, b], []], [[a, b], [a], []], 是, 是, 否, continuity_alone_does_not_identify_the_final_topology)

Wave6第十一層核對=(coarser_target, [[a, b], []], [[a, b], [a], []], 是, 是, 否, continuity_alone_does_not_identify_the_final_topology)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0086/)

商拓撲 · qf-mod48-quotient-topology-boundary · candidate





## 87. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-boundary；資料={"mode":"fiber_split","model":{"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5]],"y_points":["a","b"],"q_map":["a","a","a","b","b","b"],"subset":[0]}}。請依 [mode, source_subset, image, saturation, saturated, full_preimage_claim, boundary] 欄序回答。

四種mode為7/8/7/7欄。非滿射仍由逆像iff定義final topology，但依本節慣例不是quotient map；僅有continuity不足以唯一指定final topology。

查看答案與解釋(fiber_split, [0], [a], [0, 1, 2], 否, 否, only_saturated_subsets_are_full_preimages)

Wave6第十一層核對=(fiber_split, [0], [a], [0, 1, 2], 否, 否, only_saturated_subsets_are_full_preimages)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0087/)

商拓撲 · qf-mod48-quotient-topology-boundary · candidate





## 88. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-boundary；資料={"mode":"non_surjective","model":{"x_points":[0,1,2,3],"x_topology":[[],[2],[0,1,2,3]],"y_points":["y0","y1","y2","y3","y4"],"q_map":["y0","y1","y2","y3"]}}。請依 [mode, fibers, surjective, final_topology, final_topology_exists, quotient_map_claim, boundary] 欄序回答。

四種mode為7/8/7/7欄。非滿射仍由逆像iff定義final topology，但依本節慣例不是quotient map；僅有continuity不足以唯一指定final topology。

查看答案與解釋(non_surjective, [[y0, [0]], [y1, [1]], [y2, [2]], [y3, [3]], [y4, []]], 否, [[y0, y1, y2, y3, y4], [y0, y1, y2, y3], [y2, y4], [y2], [y4], []], 是, 否, preimage_defined_final_topology_exists_but_map_is_not_a_quotient_map_by_this_convention)

Wave6第十一層核對=(non_surjective, [[y0, [0]], [y1, [1]], [y2, [2]], [y3, [3]], [y4, []]], 否, [[y0, y1, y2, y3, y4], [y0, y1, y2, y3], [y2, y4], [y2], [y4], []], 是, 否, preimage_defined_final_topology_exists_but_map_is_not_a_quotient_map_by_this_convention)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0088/)

商拓撲 · qf-mod48-quotient-topology-boundary · candidate





## 89. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-boundary；資料={"mode":"open_image_error","model":{"x_points":[0,1,2,3,4],"x_topology":[[],[2],[0,1,2,3,4]],"y_points":["a","b"],"q_map":["a","a","a","b","b"],"subset":[2]}}。請依 [mode, source_subset, source_open, image, image_preimage, image_open, automatic_open_map_claim, boundary] 欄序回答。

四種mode為7/8/7/7欄。非滿射仍由逆像iff定義final topology，但依本節慣例不是quotient map；僅有continuity不足以唯一指定final topology。

查看答案與解釋(open_image_error, [2], 是, [a], [0, 1, 2], 否, 否, quotient_maps_need_not_be_open)

Wave6第十一層核對=(open_image_error, [2], 是, [a], [0, 1, 2], 否, 否, quotient_maps_need_not_be_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0089/)

商拓撲 · qf-mod48-quotient-topology-boundary · candidate





## 90. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-boundary；資料={"mode":"coarser_target","model":{"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,2,3,4]],"y_points":["a","b"],"q_map":["a","a","a","a","a","b"],"candidate_topology":[[],["a","b"]]}}。請依 [mode, candidate_topology, final_topology, q_continuous, properly_coarser, final_topology_identification_claim, boundary] 欄序回答。

四種mode為7/8/7/7欄。非滿射仍由逆像iff定義final topology，但依本節慣例不是quotient map；僅有continuity不足以唯一指定final topology。

查看答案與解釋(coarser_target, [[a, b], []], [[a, b], [a], []], 是, 是, 否, continuity_alone_does_not_identify_the_final_topology)

Wave6第十一層核對=(coarser_target, [[a, b], []], [[a, b], [a], []], 是, 是, 否, continuity_alone_does_not_identify_the_final_topology)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0090/)

商拓撲 · qf-mod48-quotient-topology-boundary · candidate





## 91. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-boundary；資料={"mode":"fiber_split","model":{"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5]],"y_points":["a","b"],"q_map":["a","b","b","a","b","b"],"subset":[0]}}。請依 [mode, source_subset, image, saturation, saturated, full_preimage_claim, boundary] 欄序回答。

四種mode為7/8/7/7欄。非滿射仍由逆像iff定義final topology，但依本節慣例不是quotient map；僅有continuity不足以唯一指定final topology。

查看答案與解釋(fiber_split, [0], [a], [0, 3], 否, 否, only_saturated_subsets_are_full_preimages)

Wave6第十一層核對=(fiber_split, [0], [a], [0, 3], 否, 否, only_saturated_subsets_are_full_preimages)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0091/)

商拓撲 · qf-mod48-quotient-topology-boundary · candidate





## 92. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-boundary；資料={"mode":"non_surjective","model":{"x_points":[0,1,2,3],"x_topology":[[],[0,2],[0,1,2,3]],"y_points":["y0","y1","y2","y3","y4"],"q_map":["y0","y1","y2","y3"]}}。請依 [mode, fibers, surjective, final_topology, final_topology_exists, quotient_map_claim, boundary] 欄序回答。

四種mode為7/8/7/7欄。非滿射仍由逆像iff定義final topology，但依本節慣例不是quotient map；僅有continuity不足以唯一指定final topology。

查看答案與解釋(non_surjective, [[y0, [0]], [y1, [1]], [y2, [2]], [y3, [3]], [y4, []]], 否, [[y0, y1, y2, y3, y4], [y0, y1, y2, y3], [y0, y2, y4], [y0, y2], [y4], []], 是, 否, preimage_defined_final_topology_exists_but_map_is_not_a_quotient_map_by_this_convention)

Wave6第十一層核對=(non_surjective, [[y0, [0]], [y1, [1]], [y2, [2]], [y3, [3]], [y4, []]], 否, [[y0, y1, y2, y3, y4], [y0, y1, y2, y3], [y0, y2, y4], [y0, y2], [y4], []], 是, 否, preimage_defined_final_topology_exists_but_map_is_not_a_quotient_map_by_this_convention)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0092/)

商拓撲 · qf-mod48-quotient-topology-boundary · candidate





## 93. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-boundary；資料={"mode":"open_image_error","model":{"x_points":[0,1,2,3,4],"x_topology":[[],[0,2],[0,1,2,3,4]],"y_points":["a","b"],"q_map":["a","a","a","b","b"],"subset":[0,2]}}。請依 [mode, source_subset, source_open, image, image_preimage, image_open, automatic_open_map_claim, boundary] 欄序回答。

四種mode為7/8/7/7欄。非滿射仍由逆像iff定義final topology，但依本節慣例不是quotient map；僅有continuity不足以唯一指定final topology。

查看答案與解釋(open_image_error, [0, 2], 是, [a], [0, 1, 2], 否, 否, quotient_maps_need_not_be_open)

Wave6第十一層核對=(open_image_error, [0, 2], 是, [a], [0, 1, 2], 否, 否, quotient_maps_need_not_be_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0093/)

商拓撲 · qf-mod48-quotient-topology-boundary · candidate





## 94. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-boundary；資料={"mode":"coarser_target","model":{"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,2,5]],"y_points":["a","b"],"q_map":["a","a","a","b","b","a"],"candidate_topology":[[],["a","b"]]}}。請依 [mode, candidate_topology, final_topology, q_continuous, properly_coarser, final_topology_identification_claim, boundary] 欄序回答。

四種mode為7/8/7/7欄。非滿射仍由逆像iff定義final topology，但依本節慣例不是quotient map；僅有continuity不足以唯一指定final topology。

查看答案與解釋(coarser_target, [[a, b], []], [[a, b], [a], []], 是, 是, 否, continuity_alone_does_not_identify_the_final_topology)

Wave6第十一層核對=(coarser_target, [[a, b], []], [[a, b], [a], []], 是, 是, 否, continuity_alone_does_not_identify_the_final_topology)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0094/)

商拓撲 · qf-mod48-quotient-topology-boundary · candidate





## 95. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-boundary；資料={"mode":"fiber_split","model":{"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5]],"y_points":["a","b"],"q_map":["a","a","b","a","b","b"],"subset":[0]}}。請依 [mode, source_subset, image, saturation, saturated, full_preimage_claim, boundary] 欄序回答。

四種mode為7/8/7/7欄。非滿射仍由逆像iff定義final topology，但依本節慣例不是quotient map；僅有continuity不足以唯一指定final topology。

查看答案與解釋(fiber_split, [0], [a], [0, 1, 3], 否, 否, only_saturated_subsets_are_full_preimages)

Wave6第十一層核對=(fiber_split, [0], [a], [0, 1, 3], 否, 否, only_saturated_subsets_are_full_preimages)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0095/)

商拓撲 · qf-mod48-quotient-topology-boundary · candidate





## 96. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-boundary；資料={"mode":"non_surjective","model":{"x_points":[0,1,2,3],"x_topology":[[],[1,2],[0,1,2,3]],"y_points":["y0","y1","y2","y3","y4"],"q_map":["y0","y1","y2","y3"]}}。請依 [mode, fibers, surjective, final_topology, final_topology_exists, quotient_map_claim, boundary] 欄序回答。

四種mode為7/8/7/7欄。非滿射仍由逆像iff定義final topology，但依本節慣例不是quotient map；僅有continuity不足以唯一指定final topology。

查看答案與解釋(non_surjective, [[y0, [0]], [y1, [1]], [y2, [2]], [y3, [3]], [y4, []]], 否, [[y0, y1, y2, y3, y4], [y0, y1, y2, y3], [y1, y2, y4], [y1, y2], [y4], []], 是, 否, preimage_defined_final_topology_exists_but_map_is_not_a_quotient_map_by_this_convention)

Wave6第十一層核對=(non_surjective, [[y0, [0]], [y1, [1]], [y2, [2]], [y3, [3]], [y4, []]], 否, [[y0, y1, y2, y3, y4], [y0, y1, y2, y3], [y1, y2, y4], [y1, y2], [y4], []], 是, 否, preimage_defined_final_topology_exists_but_map_is_not_a_quotient_map_by_this_convention)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0096/)

商拓撲 · qf-mod48-quotient-topology-boundary · candidate





## 97. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-boundary；資料={"mode":"open_image_error","model":{"x_points":[0,1,2,3,4],"x_topology":[[],[1,2],[0,1,2,3,4]],"y_points":["a","b"],"q_map":["a","a","a","b","b"],"subset":[1,2]}}。請依 [mode, source_subset, source_open, image, image_preimage, image_open, automatic_open_map_claim, boundary] 欄序回答。

四種mode為7/8/7/7欄。非滿射仍由逆像iff定義final topology，但依本節慣例不是quotient map；僅有continuity不足以唯一指定final topology。

查看答案與解釋(open_image_error, [1, 2], 是, [a], [0, 1, 2], 否, 否, quotient_maps_need_not_be_open)

Wave6第十一層核對=(open_image_error, [1, 2], 是, [a], [0, 1, 2], 否, 否, quotient_maps_need_not_be_open)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0097/)

商拓撲 · qf-mod48-quotient-topology-boundary · candidate





## 98. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-boundary；資料={"mode":"coarser_target","model":{"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5],[0,1,2,3,5]],"y_points":["a","b"],"q_map":["a","a","a","a","b","a"],"candidate_topology":[[],["a","b"]]}}。請依 [mode, candidate_topology, final_topology, q_continuous, properly_coarser, final_topology_identification_claim, boundary] 欄序回答。

四種mode為7/8/7/7欄。非滿射仍由逆像iff定義final topology，但依本節慣例不是quotient map；僅有continuity不足以唯一指定final topology。

查看答案與解釋(coarser_target, [[a, b], []], [[a, b], [a], []], 是, 是, 否, continuity_alone_does_not_identify_the_final_topology)

Wave6第十一層核對=(coarser_target, [[a, b], []], [[a, b], [a], []], 是, 是, 否, continuity_alone_does_not_identify_the_final_topology)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0098/)

商拓撲 · qf-mod48-quotient-topology-boundary · candidate





## 99. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-boundary；資料={"mode":"fiber_split","model":{"x_points":[0,1,2,3,4,5],"x_topology":[[],[0,1,2,3,4,5]],"y_points":["a","b"],"q_map":["a","b","a","a","b","b"],"subset":[0]}}。請依 [mode, source_subset, image, saturation, saturated, full_preimage_claim, boundary] 欄序回答。

四種mode為7/8/7/7欄。非滿射仍由逆像iff定義final topology，但依本節慣例不是quotient map；僅有continuity不足以唯一指定final topology。

查看答案與解釋(fiber_split, [0], [a], [0, 2, 3], 否, 否, only_saturated_subsets_are_full_preimages)

Wave6第十一層核對=(fiber_split, [0], [a], [0, 2, 3], 否, 否, only_saturated_subsets_are_full_preimages)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0099/)

商拓撲 · qf-mod48-quotient-topology-boundary · candidate





## 100. 商拓撲

finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-topology-boundary；資料={"mode":"non_surjective","model":{"x_points":[0,1,2,3],"x_topology":[[],[0,1,2],[0,1,2,3]],"y_points":["y0","y1","y2","y3","y4"],"q_map":["y0","y1","y2","y3"]}}。請依 [mode, fibers, surjective, final_topology, final_topology_exists, quotient_map_claim, boundary] 欄序回答。

四種mode為7/8/7/7欄。非滿射仍由逆像iff定義final topology，但依本節慣例不是quotient map；僅有continuity不足以唯一指定final topology。

查看答案與解釋(non_surjective, [[y0, [0]], [y1, [1]], [y2, [2]], [y3, [3]], [y4, []]], 否, [[y0, y1, y2, y3, y4], [y0, y1, y2, y3], [y0, y1, y2, y4], [y0, y1, y2], [y4], []], 是, 否, preimage_defined_final_topology_exists_but_map_is_not_a_quotient_map_by_this_convention)

Wave6第十一層核對=(non_surjective, [[y0, [0]], [y1, [1]], [y2, [2]], [y3, [3]], [y4, []]], 否, [[y0, y1, y2, y3, y4], [y0, y1, y2, y3], [y0, y1, y2, y4], [y0, y1, y2], [y4], []], 是, 否, preimage_defined_final_topology_exists_but_map_is_not_a_quotient_map_by_this_convention)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261117-r05-quotient-topology-0100/)

商拓撲 · qf-mod48-quotient-topology-boundary · candidate



[原始題目 JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261015-advance-20261117-r05-quotient-topology-foundations/questions.jsonl) · [驗收報告](https://ocme.evemisslab.com/data/questions/batches/batch-20261015-advance-20261117-r05-quotient-topology-foundations/validation-report.json)