# 同胚基礎 · 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-20261014-advance-20261105-r05-homeomorphism-foundations · 2026-10-14 · 100 題

欄序為來源綁定的呈現補充；原始 JSONL 與數學答案不變。

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



## 1. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-finite-topology-audit；資料={"n":5,"source_topology":[[],[0],[0,1,2],[0,1,2,3,4],[0,3,4],[1,2],[1,2,3,4],[3,4]],"target_topology":[[],[0],[0,1,2],[0,1,2,3,4],[0,3,4],[1,2],[1,2,3,4],[3,4]],"map":[0,1,2,3,4]}。請依 [source_topology_valid, target_topology_valid, bijection, forward_continuous, inverse_continuous, homeomorphism, certificate] 欄序回答。

查看答案與解釋(是, 是, 是, 是, 是, 是, complete_open_set_preimage_audit)

Wave5第五層核對=(是, 是, 是, 是, 是, 是, complete_open_set_preimage_audit)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0001/)

同胚 · qf-mod36-homeo-finite-topology-audit · candidate





## 2. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-finite-topology-audit；資料={"n":5,"source_topology":[[],[0],[0,1,2],[0,1,2,3,4],[0,3,4],[1,2],[1,2,3,4],[3,4]],"target_topology":[[],[0],[0,1,2],[0,1,2,3,4],[0,3,4],[1,2],[1,2,3,4],[3,4]],"map":[0,1,2,4,3]}。請依 [source_topology_valid, target_topology_valid, bijection, forward_continuous, inverse_continuous, homeomorphism, certificate] 欄序回答。

查看答案與解釋(是, 是, 是, 是, 是, 是, complete_open_set_preimage_audit)

Wave5第五層核對=(是, 是, 是, 是, 是, 是, complete_open_set_preimage_audit)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0002/)

同胚 · qf-mod36-homeo-finite-topology-audit · candidate





## 3. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-finite-topology-audit；資料={"n":5,"source_topology":[[],[0],[0,1,2],[0,1,2,3,4],[0,3,4],[1,2],[1,2,3,4],[3,4]],"target_topology":[[],[0],[0,1,2,3,4],[0,1,3],[0,2,4],[1,2,3,4],[1,3],[2,4]],"map":[0,1,3,2,4]}。請依 [source_topology_valid, target_topology_valid, bijection, forward_continuous, inverse_continuous, homeomorphism, certificate] 欄序回答。

查看答案與解釋(是, 是, 是, 是, 是, 是, complete_open_set_preimage_audit)

Wave5第五層核對=(是, 是, 是, 是, 是, 是, complete_open_set_preimage_audit)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0003/)

同胚 · qf-mod36-homeo-finite-topology-audit · candidate





## 4. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-finite-topology-audit；資料={"n":5,"source_topology":[[],[0],[0,1,2],[0,1,2,3,4],[0,3,4],[1,2],[1,2,3,4],[3,4]],"target_topology":[[],[0],[0,1,2,3,4],[0,1,3],[0,2,4],[1,2,3,4],[1,3],[2,4]],"map":[0,1,3,4,2]}。請依 [source_topology_valid, target_topology_valid, bijection, forward_continuous, inverse_continuous, homeomorphism, certificate] 欄序回答。

查看答案與解釋(是, 是, 是, 是, 是, 是, complete_open_set_preimage_audit)

Wave5第五層核對=(是, 是, 是, 是, 是, 是, complete_open_set_preimage_audit)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0004/)

同胚 · qf-mod36-homeo-finite-topology-audit · candidate





## 5. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-finite-topology-audit；資料={"n":5,"source_topology":[[],[0],[0,1,2],[0,1,2,3,4],[0,3,4],[1,2],[1,2,3,4],[3,4]],"target_topology":[[],[0],[0,1,2,3,4],[0,1,4],[0,2,3],[1,2,3,4],[1,4],[2,3]],"map":[0,1,4,2,3]}。請依 [source_topology_valid, target_topology_valid, bijection, forward_continuous, inverse_continuous, homeomorphism, certificate] 欄序回答。

查看答案與解釋(是, 是, 是, 是, 是, 是, complete_open_set_preimage_audit)

Wave5第五層核對=(是, 是, 是, 是, 是, 是, complete_open_set_preimage_audit)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0005/)

同胚 · qf-mod36-homeo-finite-topology-audit · candidate





## 6. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-finite-topology-audit；資料={"n":5,"source_topology":[[],[0],[0,1,2],[0,1,2,3,4],[0,3,4],[1,2],[1,2,3,4],[3,4]],"target_topology":[[],[0],[0,1,2,3,4],[0,1,4],[0,2,3],[1,2,3,4],[1,4],[2,3]],"map":[0,1,4,3,2]}。請依 [source_topology_valid, target_topology_valid, bijection, forward_continuous, inverse_continuous, homeomorphism, certificate] 欄序回答。

查看答案與解釋(是, 是, 是, 是, 是, 是, complete_open_set_preimage_audit)

Wave5第五層核對=(是, 是, 是, 是, 是, 是, complete_open_set_preimage_audit)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0006/)

同胚 · qf-mod36-homeo-finite-topology-audit · candidate





## 7. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-finite-topology-audit；資料={"n":5,"source_topology":[[],[0],[0,1,2],[0,1,2,3,4],[0,3,4],[1,2],[1,2,3,4],[3,4]],"target_topology":[[],[0],[0,1,2],[0,1,2,3,4],[0,3,4],[1,2],[1,2,3,4],[3,4]],"map":[0,2,1,3,4]}。請依 [source_topology_valid, target_topology_valid, bijection, forward_continuous, inverse_continuous, homeomorphism, certificate] 欄序回答。

查看答案與解釋(是, 是, 是, 是, 是, 是, complete_open_set_preimage_audit)

Wave5第五層核對=(是, 是, 是, 是, 是, 是, complete_open_set_preimage_audit)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0007/)

同胚 · qf-mod36-homeo-finite-topology-audit · candidate





## 8. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-finite-topology-audit；資料={"n":5,"source_topology":[[],[0],[0,1,2],[0,1,2,3,4],[0,3,4],[1,2],[1,2,3,4],[3,4]],"target_topology":[[],[0],[0,1,2],[0,1,2,3,4],[0,3,4],[1,2],[1,2,3,4],[3,4]],"map":[0,2,1,4,3]}。請依 [source_topology_valid, target_topology_valid, bijection, forward_continuous, inverse_continuous, homeomorphism, certificate] 欄序回答。

查看答案與解釋(是, 是, 是, 是, 是, 是, complete_open_set_preimage_audit)

Wave5第五層核對=(是, 是, 是, 是, 是, 是, complete_open_set_preimage_audit)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0008/)

同胚 · qf-mod36-homeo-finite-topology-audit · candidate





## 9. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-finite-topology-audit；資料={"n":5,"source_topology":[[],[0],[0,1,2],[0,1,2,3,4],[0,3,4],[1,2],[1,2,3,4],[3,4]],"target_topology":[[],[0],[0,1,2,3,4],[0,1,4],[0,2,3],[1,2,3,4],[1,4],[2,3]],"map":[0,2,3,1,4]}。請依 [source_topology_valid, target_topology_valid, bijection, forward_continuous, inverse_continuous, homeomorphism, certificate] 欄序回答。

查看答案與解釋(是, 是, 是, 是, 是, 是, complete_open_set_preimage_audit)

Wave5第五層核對=(是, 是, 是, 是, 是, 是, complete_open_set_preimage_audit)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0009/)

同胚 · qf-mod36-homeo-finite-topology-audit · candidate





## 10. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-finite-topology-audit；資料={"n":5,"source_topology":[[],[0],[0,1,2],[0,1,2,3,4],[0,3,4],[1,2],[1,2,3,4],[3,4]],"target_topology":[[],[0],[0,1,2,3,4],[0,1,4],[0,2,3],[1,2,3,4],[1,4],[2,3]],"map":[0,2,3,4,1]}。請依 [source_topology_valid, target_topology_valid, bijection, forward_continuous, inverse_continuous, homeomorphism, certificate] 欄序回答。

查看答案與解釋(是, 是, 是, 是, 是, 是, complete_open_set_preimage_audit)

Wave5第五層核對=(是, 是, 是, 是, 是, 是, complete_open_set_preimage_audit)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0010/)

同胚 · qf-mod36-homeo-finite-topology-audit · candidate





## 11. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-finite-topology-audit；資料={"n":5,"source_topology":[[],[0],[0,1,2],[0,1,2,3,4],[0,3,4],[1,2],[1,2,3,4],[3,4]],"target_topology":[[],[0],[0,1,2,3,4],[0,1,3],[0,2,4],[1,2,3,4],[1,3],[2,4]],"map":[0,2,4,1,3]}。請依 [source_topology_valid, target_topology_valid, bijection, forward_continuous, inverse_continuous, homeomorphism, certificate] 欄序回答。

查看答案與解釋(是, 是, 是, 是, 是, 是, complete_open_set_preimage_audit)

Wave5第五層核對=(是, 是, 是, 是, 是, 是, complete_open_set_preimage_audit)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0011/)

同胚 · qf-mod36-homeo-finite-topology-audit · candidate





## 12. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-finite-topology-audit；資料={"n":5,"source_topology":[[],[0],[0,1,2],[0,1,2,3,4],[0,3,4],[1,2],[1,2,3,4],[3,4]],"target_topology":[[],[0],[0,1,2,3,4],[0,1,3],[0,2,4],[1,2,3,4],[1,3],[2,4]],"map":[0,2,4,3,1]}。請依 [source_topology_valid, target_topology_valid, bijection, forward_continuous, inverse_continuous, homeomorphism, certificate] 欄序回答。

查看答案與解釋(是, 是, 是, 是, 是, 是, complete_open_set_preimage_audit)

Wave5第五層核對=(是, 是, 是, 是, 是, 是, complete_open_set_preimage_audit)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0012/)

同胚 · qf-mod36-homeo-finite-topology-audit · candidate





## 13. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-finite-topology-audit；資料={"n":5,"source_topology":[[],[0],[0,1,2],[0,1,2,3,4],[0,3,4],[1,2],[1,2,3,4],[3,4]],"target_topology":[[],[0],[0,1,2,3,4],[0,1,3],[0,2,4],[1,2,3,4],[1,3],[2,4]],"map":[0,3,1,2,4]}。請依 [source_topology_valid, target_topology_valid, bijection, forward_continuous, inverse_continuous, homeomorphism, certificate] 欄序回答。

查看答案與解釋(是, 是, 是, 是, 是, 是, complete_open_set_preimage_audit)

Wave5第五層核對=(是, 是, 是, 是, 是, 是, complete_open_set_preimage_audit)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0013/)

同胚 · qf-mod36-homeo-finite-topology-audit · candidate





## 14. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-finite-topology-audit；資料={"n":5,"source_topology":[[],[0],[0,1,2],[0,1,2,3,4],[0,3,4],[1,2],[1,2,3,4],[3,4]],"target_topology":[[],[0],[0,1,2,3,4],[0,1,3],[0,2,4],[1,2,3,4],[1,3],[2,4]],"map":[0,3,1,4,2]}。請依 [source_topology_valid, target_topology_valid, bijection, forward_continuous, inverse_continuous, homeomorphism, certificate] 欄序回答。

查看答案與解釋(是, 是, 是, 是, 是, 是, complete_open_set_preimage_audit)

Wave5第五層核對=(是, 是, 是, 是, 是, 是, complete_open_set_preimage_audit)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0014/)

同胚 · qf-mod36-homeo-finite-topology-audit · candidate





## 15. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-finite-topology-audit；資料={"n":5,"source_topology":[[],[0],[0,1,2],[0,1,2,3,4],[0,3,4],[1,2],[1,2,3,4],[3,4]],"target_topology":[[],[0],[0,1,2,3,4],[0,1,4],[0,2,3],[1,2,3,4],[1,4],[2,3]],"map":[0,3,2,1,4]}。請依 [source_topology_valid, target_topology_valid, bijection, forward_continuous, inverse_continuous, homeomorphism, certificate] 欄序回答。

查看答案與解釋(是, 是, 是, 是, 是, 是, complete_open_set_preimage_audit)

Wave5第五層核對=(是, 是, 是, 是, 是, 是, complete_open_set_preimage_audit)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0015/)

同胚 · qf-mod36-homeo-finite-topology-audit · candidate





## 16. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-finite-topology-audit；資料={"n":5,"source_topology":[[],[0],[0,1,2],[0,1,2,3,4],[0,3,4],[1,2],[1,2,3,4],[3,4]],"target_topology":[[],[0],[0,1,2,3,4],[0,1,4],[0,2,3],[1,2,3,4],[1,4],[2,3]],"map":[0,3,2,4,1]}。請依 [source_topology_valid, target_topology_valid, bijection, forward_continuous, inverse_continuous, homeomorphism, certificate] 欄序回答。

查看答案與解釋(是, 是, 是, 是, 是, 是, complete_open_set_preimage_audit)

Wave5第五層核對=(是, 是, 是, 是, 是, 是, complete_open_set_preimage_audit)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0016/)

同胚 · qf-mod36-homeo-finite-topology-audit · candidate





## 17. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-finite-topology-audit；資料={"n":5,"source_topology":[[],[0],[0,1,2],[0,1,2,3,4],[0,3,4],[1,2],[1,2,3,4],[3,4]],"target_topology":[[],[0],[0,1,2],[0,1,2,3,4],[0,3,4],[1,2],[1,2,3,4],[3,4]],"map":[0,3,4,1,2]}。請依 [source_topology_valid, target_topology_valid, bijection, forward_continuous, inverse_continuous, homeomorphism, certificate] 欄序回答。

查看答案與解釋(是, 是, 是, 是, 是, 是, complete_open_set_preimage_audit)

Wave5第五層核對=(是, 是, 是, 是, 是, 是, complete_open_set_preimage_audit)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0017/)

同胚 · qf-mod36-homeo-finite-topology-audit · candidate





## 18. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-finite-topology-audit；資料={"n":5,"source_topology":[[],[0],[0,1,2],[0,1,2,3,4],[0,3,4],[1,2],[1,2,3,4],[3,4]],"target_topology":[[],[0],[0,1,2],[0,1,2,3,4],[0,3,4],[1,2],[1,2,3,4],[3,4]],"map":[0,3,4,2,1]}。請依 [source_topology_valid, target_topology_valid, bijection, forward_continuous, inverse_continuous, homeomorphism, certificate] 欄序回答。

查看答案與解釋(是, 是, 是, 是, 是, 是, complete_open_set_preimage_audit)

Wave5第五層核對=(是, 是, 是, 是, 是, 是, complete_open_set_preimage_audit)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0018/)

同胚 · qf-mod36-homeo-finite-topology-audit · candidate





## 19. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-finite-topology-audit；資料={"n":5,"source_topology":[[],[0],[0,1,2],[0,1,2,3,4],[0,3,4],[1,2],[1,2,3,4],[3,4]],"target_topology":[[],[0],[0,1,2,3,4],[0,1,4],[0,2,3],[1,2,3,4],[1,4],[2,3]],"map":[0,4,1,2,3]}。請依 [source_topology_valid, target_topology_valid, bijection, forward_continuous, inverse_continuous, homeomorphism, certificate] 欄序回答。

查看答案與解釋(是, 是, 是, 是, 是, 是, complete_open_set_preimage_audit)

Wave5第五層核對=(是, 是, 是, 是, 是, 是, complete_open_set_preimage_audit)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0019/)

同胚 · qf-mod36-homeo-finite-topology-audit · candidate





## 20. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-finite-topology-audit；資料={"n":5,"source_topology":[[],[0],[0,1,2],[0,1,2,3,4],[0,3,4],[1,2],[1,2,3,4],[3,4]],"target_topology":[[],[0],[0,1,2,3,4],[0,1,4],[0,2,3],[1,2,3,4],[1,4],[2,3]],"map":[0,4,1,3,2]}。請依 [source_topology_valid, target_topology_valid, bijection, forward_continuous, inverse_continuous, homeomorphism, certificate] 欄序回答。

查看答案與解釋(是, 是, 是, 是, 是, 是, complete_open_set_preimage_audit)

Wave5第五層核對=(是, 是, 是, 是, 是, 是, complete_open_set_preimage_audit)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0020/)

同胚 · qf-mod36-homeo-finite-topology-audit · candidate





## 21. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-finite-topology-audit；資料={"n":5,"source_topology":[[],[0],[0,1,2],[0,1,2,3,4],[0,3,4],[1,2],[1,2,3,4],[3,4]],"target_topology":[[],[0],[0,1,2,3,4],[0,1,3],[0,2,4],[1,2,3,4],[1,3],[2,4]],"map":[0,4,2,1,3]}。請依 [source_topology_valid, target_topology_valid, bijection, forward_continuous, inverse_continuous, homeomorphism, certificate] 欄序回答。

查看答案與解釋(是, 是, 是, 是, 是, 是, complete_open_set_preimage_audit)

Wave5第五層核對=(是, 是, 是, 是, 是, 是, complete_open_set_preimage_audit)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0021/)

同胚 · qf-mod36-homeo-finite-topology-audit · candidate





## 22. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-finite-topology-audit；資料={"n":5,"source_topology":[[],[0],[0,1,2],[0,1,2,3,4],[0,3,4],[1,2],[1,2,3,4],[3,4]],"target_topology":[[],[0],[0,1,2,3,4],[0,1,3],[0,2,4],[1,2,3,4],[1,3],[2,4]],"map":[0,4,2,3,1]}。請依 [source_topology_valid, target_topology_valid, bijection, forward_continuous, inverse_continuous, homeomorphism, certificate] 欄序回答。

查看答案與解釋(是, 是, 是, 是, 是, 是, complete_open_set_preimage_audit)

Wave5第五層核對=(是, 是, 是, 是, 是, 是, complete_open_set_preimage_audit)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0022/)

同胚 · qf-mod36-homeo-finite-topology-audit · candidate





## 23. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-finite-topology-audit；資料={"n":5,"source_topology":[[],[0],[0,1,2],[0,1,2,3,4],[0,3,4],[1,2],[1,2,3,4],[3,4]],"target_topology":[[],[0],[0,1,2],[0,1,2,3,4],[0,3,4],[1,2],[1,2,3,4],[3,4]],"map":[0,4,3,1,2]}。請依 [source_topology_valid, target_topology_valid, bijection, forward_continuous, inverse_continuous, homeomorphism, certificate] 欄序回答。

查看答案與解釋(是, 是, 是, 是, 是, 是, complete_open_set_preimage_audit)

Wave5第五層核對=(是, 是, 是, 是, 是, 是, complete_open_set_preimage_audit)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0023/)

同胚 · qf-mod36-homeo-finite-topology-audit · candidate





## 24. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-finite-topology-audit；資料={"n":5,"source_topology":[[],[0],[0,1,2],[0,1,2,3,4],[0,3,4],[1,2],[1,2,3,4],[3,4]],"target_topology":[[],[0],[0,1,2],[0,1,2,3,4],[0,3,4],[1,2],[1,2,3,4],[3,4]],"map":[0,4,3,2,1]}。請依 [source_topology_valid, target_topology_valid, bijection, forward_continuous, inverse_continuous, homeomorphism, certificate] 欄序回答。

查看答案與解釋(是, 是, 是, 是, 是, 是, complete_open_set_preimage_audit)

Wave5第五層核對=(是, 是, 是, 是, 是, 是, complete_open_set_preimage_audit)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0024/)

同胚 · qf-mod36-homeo-finite-topology-audit · candidate





## 25. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-finite-topology-audit；資料={"n":5,"source_topology":[[],[0],[0,1,2],[0,1,2,3,4],[0,3,4],[1,2],[1,2,3,4],[3,4]],"target_topology":[[],[0,1,2],[0,1,2,3,4],[0,2],[0,2,3,4],[1],[1,3,4],[3,4]],"map":[1,0,2,3,4]}。請依 [source_topology_valid, target_topology_valid, bijection, forward_continuous, inverse_continuous, homeomorphism, certificate] 欄序回答。

查看答案與解釋(是, 是, 是, 是, 是, 是, complete_open_set_preimage_audit)

Wave5第五層核對=(是, 是, 是, 是, 是, 是, complete_open_set_preimage_audit)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0025/)

同胚 · qf-mod36-homeo-finite-topology-audit · candidate





## 26. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-continuous-bijection-boundary；資料={"n":5,"source_topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]],"target_topology":[[],[0,1,2,3,4]],"map":[0,1,2,3,4]}。請依 [source_topology_valid, target_topology_valid, bijection, forward_continuous, inverse_continuous, homeomorphism, boundary] 欄序回答。

查看答案與解釋(是, 是, 是, 是, 否, 否, continuous_bijection_inverse_continuity_required)

Wave5第五層核對=(是, 是, 是, 是, 否, 否, continuous_bijection_inverse_continuity_required)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0026/)

同胚 · qf-mod36-homeo-continuous-bijection-boundary · candidate





## 27. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-continuous-bijection-boundary；資料={"n":5,"source_topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]],"target_topology":[[],[0,1,2,3,4]],"map":[0,1,2,4,3]}。請依 [source_topology_valid, target_topology_valid, bijection, forward_continuous, inverse_continuous, homeomorphism, boundary] 欄序回答。

查看答案與解釋(是, 是, 是, 是, 否, 否, continuous_bijection_inverse_continuity_required)

Wave5第五層核對=(是, 是, 是, 是, 否, 否, continuous_bijection_inverse_continuity_required)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0027/)

同胚 · qf-mod36-homeo-continuous-bijection-boundary · candidate





## 28. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-continuous-bijection-boundary；資料={"n":5,"source_topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]],"target_topology":[[],[0,1,2,3,4]],"map":[0,1,3,2,4]}。請依 [source_topology_valid, target_topology_valid, bijection, forward_continuous, inverse_continuous, homeomorphism, boundary] 欄序回答。

查看答案與解釋(是, 是, 是, 是, 否, 否, continuous_bijection_inverse_continuity_required)

Wave5第五層核對=(是, 是, 是, 是, 否, 否, continuous_bijection_inverse_continuity_required)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0028/)

同胚 · qf-mod36-homeo-continuous-bijection-boundary · candidate





## 29. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-continuous-bijection-boundary；資料={"n":5,"source_topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]],"target_topology":[[],[0,1,2,3,4]],"map":[0,1,3,4,2]}。請依 [source_topology_valid, target_topology_valid, bijection, forward_continuous, inverse_continuous, homeomorphism, boundary] 欄序回答。

查看答案與解釋(是, 是, 是, 是, 否, 否, continuous_bijection_inverse_continuity_required)

Wave5第五層核對=(是, 是, 是, 是, 否, 否, continuous_bijection_inverse_continuity_required)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0029/)

同胚 · qf-mod36-homeo-continuous-bijection-boundary · candidate





## 30. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-continuous-bijection-boundary；資料={"n":5,"source_topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]],"target_topology":[[],[0,1,2,3,4]],"map":[0,1,4,2,3]}。請依 [source_topology_valid, target_topology_valid, bijection, forward_continuous, inverse_continuous, homeomorphism, boundary] 欄序回答。

查看答案與解釋(是, 是, 是, 是, 否, 否, continuous_bijection_inverse_continuity_required)

Wave5第五層核對=(是, 是, 是, 是, 否, 否, continuous_bijection_inverse_continuity_required)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0030/)

同胚 · qf-mod36-homeo-continuous-bijection-boundary · candidate





## 31. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-continuous-bijection-boundary；資料={"n":5,"source_topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]],"target_topology":[[],[0,1,2,3,4]],"map":[0,1,4,3,2]}。請依 [source_topology_valid, target_topology_valid, bijection, forward_continuous, inverse_continuous, homeomorphism, boundary] 欄序回答。

查看答案與解釋(是, 是, 是, 是, 否, 否, continuous_bijection_inverse_continuity_required)

Wave5第五層核對=(是, 是, 是, 是, 否, 否, continuous_bijection_inverse_continuity_required)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0031/)

同胚 · qf-mod36-homeo-continuous-bijection-boundary · candidate





## 32. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-continuous-bijection-boundary；資料={"n":5,"source_topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]],"target_topology":[[],[0,1,2,3,4]],"map":[0,2,1,3,4]}。請依 [source_topology_valid, target_topology_valid, bijection, forward_continuous, inverse_continuous, homeomorphism, boundary] 欄序回答。

查看答案與解釋(是, 是, 是, 是, 否, 否, continuous_bijection_inverse_continuity_required)

Wave5第五層核對=(是, 是, 是, 是, 否, 否, continuous_bijection_inverse_continuity_required)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0032/)

同胚 · qf-mod36-homeo-continuous-bijection-boundary · candidate





## 33. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-continuous-bijection-boundary；資料={"n":5,"source_topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]],"target_topology":[[],[0,1,2,3,4]],"map":[0,2,1,4,3]}。請依 [source_topology_valid, target_topology_valid, bijection, forward_continuous, inverse_continuous, homeomorphism, boundary] 欄序回答。

查看答案與解釋(是, 是, 是, 是, 否, 否, continuous_bijection_inverse_continuity_required)

Wave5第五層核對=(是, 是, 是, 是, 否, 否, continuous_bijection_inverse_continuity_required)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0033/)

同胚 · qf-mod36-homeo-continuous-bijection-boundary · candidate





## 34. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-continuous-bijection-boundary；資料={"n":5,"source_topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]],"target_topology":[[],[0,1,2,3,4]],"map":[0,2,3,1,4]}。請依 [source_topology_valid, target_topology_valid, bijection, forward_continuous, inverse_continuous, homeomorphism, boundary] 欄序回答。

查看答案與解釋(是, 是, 是, 是, 否, 否, continuous_bijection_inverse_continuity_required)

Wave5第五層核對=(是, 是, 是, 是, 否, 否, continuous_bijection_inverse_continuity_required)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0034/)

同胚 · qf-mod36-homeo-continuous-bijection-boundary · candidate





## 35. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-continuous-bijection-boundary；資料={"n":5,"source_topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]],"target_topology":[[],[0,1,2,3,4]],"map":[0,2,3,4,1]}。請依 [source_topology_valid, target_topology_valid, bijection, forward_continuous, inverse_continuous, homeomorphism, boundary] 欄序回答。

查看答案與解釋(是, 是, 是, 是, 否, 否, continuous_bijection_inverse_continuity_required)

Wave5第五層核對=(是, 是, 是, 是, 否, 否, continuous_bijection_inverse_continuity_required)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0035/)

同胚 · qf-mod36-homeo-continuous-bijection-boundary · candidate





## 36. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-continuous-bijection-boundary；資料={"n":5,"source_topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]],"target_topology":[[],[0,1,2,3,4]],"map":[0,2,4,1,3]}。請依 [source_topology_valid, target_topology_valid, bijection, forward_continuous, inverse_continuous, homeomorphism, boundary] 欄序回答。

查看答案與解釋(是, 是, 是, 是, 否, 否, continuous_bijection_inverse_continuity_required)

Wave5第五層核對=(是, 是, 是, 是, 否, 否, continuous_bijection_inverse_continuity_required)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0036/)

同胚 · qf-mod36-homeo-continuous-bijection-boundary · candidate





## 37. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-continuous-bijection-boundary；資料={"n":5,"source_topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]],"target_topology":[[],[0,1,2,3,4]],"map":[0,2,4,3,1]}。請依 [source_topology_valid, target_topology_valid, bijection, forward_continuous, inverse_continuous, homeomorphism, boundary] 欄序回答。

查看答案與解釋(是, 是, 是, 是, 否, 否, continuous_bijection_inverse_continuity_required)

Wave5第五層核對=(是, 是, 是, 是, 否, 否, continuous_bijection_inverse_continuity_required)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0037/)

同胚 · qf-mod36-homeo-continuous-bijection-boundary · candidate





## 38. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-continuous-bijection-boundary；資料={"n":5,"source_topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]],"target_topology":[[],[0,1,2,3,4]],"map":[0,3,1,2,4]}。請依 [source_topology_valid, target_topology_valid, bijection, forward_continuous, inverse_continuous, homeomorphism, boundary] 欄序回答。

查看答案與解釋(是, 是, 是, 是, 否, 否, continuous_bijection_inverse_continuity_required)

Wave5第五層核對=(是, 是, 是, 是, 否, 否, continuous_bijection_inverse_continuity_required)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0038/)

同胚 · qf-mod36-homeo-continuous-bijection-boundary · candidate





## 39. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-continuous-bijection-boundary；資料={"n":5,"source_topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]],"target_topology":[[],[0,1,2,3,4]],"map":[0,3,1,4,2]}。請依 [source_topology_valid, target_topology_valid, bijection, forward_continuous, inverse_continuous, homeomorphism, boundary] 欄序回答。

查看答案與解釋(是, 是, 是, 是, 否, 否, continuous_bijection_inverse_continuity_required)

Wave5第五層核對=(是, 是, 是, 是, 否, 否, continuous_bijection_inverse_continuity_required)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0039/)

同胚 · qf-mod36-homeo-continuous-bijection-boundary · candidate





## 40. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-continuous-bijection-boundary；資料={"n":5,"source_topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]],"target_topology":[[],[0,1,2,3,4]],"map":[0,3,2,1,4]}。請依 [source_topology_valid, target_topology_valid, bijection, forward_continuous, inverse_continuous, homeomorphism, boundary] 欄序回答。

查看答案與解釋(是, 是, 是, 是, 否, 否, continuous_bijection_inverse_continuity_required)

Wave5第五層核對=(是, 是, 是, 是, 否, 否, continuous_bijection_inverse_continuity_required)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0040/)

同胚 · qf-mod36-homeo-continuous-bijection-boundary · candidate





## 41. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-continuous-bijection-boundary；資料={"n":5,"source_topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]],"target_topology":[[],[0,1,2,3,4]],"map":[0,3,2,4,1]}。請依 [source_topology_valid, target_topology_valid, bijection, forward_continuous, inverse_continuous, homeomorphism, boundary] 欄序回答。

查看答案與解釋(是, 是, 是, 是, 否, 否, continuous_bijection_inverse_continuity_required)

Wave5第五層核對=(是, 是, 是, 是, 否, 否, continuous_bijection_inverse_continuity_required)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0041/)

同胚 · qf-mod36-homeo-continuous-bijection-boundary · candidate





## 42. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-continuous-bijection-boundary；資料={"n":5,"source_topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]],"target_topology":[[],[0,1,2,3,4]],"map":[0,3,4,1,2]}。請依 [source_topology_valid, target_topology_valid, bijection, forward_continuous, inverse_continuous, homeomorphism, boundary] 欄序回答。

查看答案與解釋(是, 是, 是, 是, 否, 否, continuous_bijection_inverse_continuity_required)

Wave5第五層核對=(是, 是, 是, 是, 否, 否, continuous_bijection_inverse_continuity_required)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0042/)

同胚 · qf-mod36-homeo-continuous-bijection-boundary · candidate





## 43. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-continuous-bijection-boundary；資料={"n":5,"source_topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]],"target_topology":[[],[0,1,2,3,4]],"map":[0,3,4,2,1]}。請依 [source_topology_valid, target_topology_valid, bijection, forward_continuous, inverse_continuous, homeomorphism, boundary] 欄序回答。

查看答案與解釋(是, 是, 是, 是, 否, 否, continuous_bijection_inverse_continuity_required)

Wave5第五層核對=(是, 是, 是, 是, 否, 否, continuous_bijection_inverse_continuity_required)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0043/)

同胚 · qf-mod36-homeo-continuous-bijection-boundary · candidate





## 44. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-continuous-bijection-boundary；資料={"n":5,"source_topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]],"target_topology":[[],[0,1,2,3,4]],"map":[0,4,1,2,3]}。請依 [source_topology_valid, target_topology_valid, bijection, forward_continuous, inverse_continuous, homeomorphism, boundary] 欄序回答。

查看答案與解釋(是, 是, 是, 是, 否, 否, continuous_bijection_inverse_continuity_required)

Wave5第五層核對=(是, 是, 是, 是, 否, 否, continuous_bijection_inverse_continuity_required)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0044/)

同胚 · qf-mod36-homeo-continuous-bijection-boundary · candidate





## 45. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-continuous-bijection-boundary；資料={"n":5,"source_topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]],"target_topology":[[],[0,1,2,3,4]],"map":[0,4,1,3,2]}。請依 [source_topology_valid, target_topology_valid, bijection, forward_continuous, inverse_continuous, homeomorphism, boundary] 欄序回答。

查看答案與解釋(是, 是, 是, 是, 否, 否, continuous_bijection_inverse_continuity_required)

Wave5第五層核對=(是, 是, 是, 是, 否, 否, continuous_bijection_inverse_continuity_required)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0045/)

同胚 · qf-mod36-homeo-continuous-bijection-boundary · candidate





## 46. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-continuous-bijection-boundary；資料={"n":5,"source_topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]],"target_topology":[[],[0,1,2,3,4]],"map":[0,4,2,1,3]}。請依 [source_topology_valid, target_topology_valid, bijection, forward_continuous, inverse_continuous, homeomorphism, boundary] 欄序回答。

查看答案與解釋(是, 是, 是, 是, 否, 否, continuous_bijection_inverse_continuity_required)

Wave5第五層核對=(是, 是, 是, 是, 否, 否, continuous_bijection_inverse_continuity_required)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0046/)

同胚 · qf-mod36-homeo-continuous-bijection-boundary · candidate





## 47. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-continuous-bijection-boundary；資料={"n":5,"source_topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]],"target_topology":[[],[0,1,2,3,4]],"map":[0,4,2,3,1]}。請依 [source_topology_valid, target_topology_valid, bijection, forward_continuous, inverse_continuous, homeomorphism, boundary] 欄序回答。

查看答案與解釋(是, 是, 是, 是, 否, 否, continuous_bijection_inverse_continuity_required)

Wave5第五層核對=(是, 是, 是, 是, 否, 否, continuous_bijection_inverse_continuity_required)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0047/)

同胚 · qf-mod36-homeo-continuous-bijection-boundary · candidate





## 48. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-continuous-bijection-boundary；資料={"n":5,"source_topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]],"target_topology":[[],[0,1,2,3,4]],"map":[0,4,3,1,2]}。請依 [source_topology_valid, target_topology_valid, bijection, forward_continuous, inverse_continuous, homeomorphism, boundary] 欄序回答。

查看答案與解釋(是, 是, 是, 是, 否, 否, continuous_bijection_inverse_continuity_required)

Wave5第五層核對=(是, 是, 是, 是, 否, 否, continuous_bijection_inverse_continuity_required)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0048/)

同胚 · qf-mod36-homeo-continuous-bijection-boundary · candidate





## 49. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-continuous-bijection-boundary；資料={"n":5,"source_topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]],"target_topology":[[],[0,1,2,3,4]],"map":[0,4,3,2,1]}。請依 [source_topology_valid, target_topology_valid, bijection, forward_continuous, inverse_continuous, homeomorphism, boundary] 欄序回答。

查看答案與解釋(是, 是, 是, 是, 否, 否, continuous_bijection_inverse_continuity_required)

Wave5第五層核對=(是, 是, 是, 是, 否, 否, continuous_bijection_inverse_continuity_required)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0049/)

同胚 · qf-mod36-homeo-continuous-bijection-boundary · candidate





## 50. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-continuous-bijection-boundary；資料={"n":5,"source_topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]],"target_topology":[[],[0,1,2,3,4]],"map":[1,0,2,3,4]}。請依 [source_topology_valid, target_topology_valid, bijection, forward_continuous, inverse_continuous, homeomorphism, boundary] 欄序回答。

查看答案與解釋(是, 是, 是, 是, 否, 否, continuous_bijection_inverse_continuity_required)

Wave5第五層核對=(是, 是, 是, 是, 否, 否, continuous_bijection_inverse_continuity_required)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0050/)

同胚 · qf-mod36-homeo-continuous-bijection-boundary · candidate





## 51. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-finite-discrete-bijection；資料={"n":5,"map":[0,1,2,3,4]}。請依 [vertex_count, map, forward_continuous, inverse_continuous, homeomorphism, boundary] 欄序回答。

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

Wave5第五層核對=(5, [0, 1, 2, 3, 4], 是, 是, 是, finite_discrete_scope_only)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0051/)

同胚 · qf-mod36-homeo-finite-discrete-bijection · candidate





## 52. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-finite-discrete-bijection；資料={"n":5,"map":[0,1,2,4,3]}。請依 [vertex_count, map, forward_continuous, inverse_continuous, homeomorphism, boundary] 欄序回答。

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

Wave5第五層核對=(5, [0, 1, 2, 4, 3], 是, 是, 是, finite_discrete_scope_only)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0052/)

同胚 · qf-mod36-homeo-finite-discrete-bijection · candidate





## 53. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-finite-discrete-bijection；資料={"n":5,"map":[0,1,3,2,4]}。請依 [vertex_count, map, forward_continuous, inverse_continuous, homeomorphism, boundary] 欄序回答。

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

Wave5第五層核對=(5, [0, 1, 3, 2, 4], 是, 是, 是, finite_discrete_scope_only)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0053/)

同胚 · qf-mod36-homeo-finite-discrete-bijection · candidate





## 54. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-finite-discrete-bijection；資料={"n":5,"map":[0,1,3,4,2]}。請依 [vertex_count, map, forward_continuous, inverse_continuous, homeomorphism, boundary] 欄序回答。

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

Wave5第五層核對=(5, [0, 1, 3, 4, 2], 是, 是, 是, finite_discrete_scope_only)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0054/)

同胚 · qf-mod36-homeo-finite-discrete-bijection · candidate





## 55. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-finite-discrete-bijection；資料={"n":5,"map":[0,1,4,2,3]}。請依 [vertex_count, map, forward_continuous, inverse_continuous, homeomorphism, boundary] 欄序回答。

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

Wave5第五層核對=(5, [0, 1, 4, 2, 3], 是, 是, 是, finite_discrete_scope_only)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0055/)

同胚 · qf-mod36-homeo-finite-discrete-bijection · candidate





## 56. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-finite-discrete-bijection；資料={"n":5,"map":[0,1,4,3,2]}。請依 [vertex_count, map, forward_continuous, inverse_continuous, homeomorphism, boundary] 欄序回答。

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

Wave5第五層核對=(5, [0, 1, 4, 3, 2], 是, 是, 是, finite_discrete_scope_only)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0056/)

同胚 · qf-mod36-homeo-finite-discrete-bijection · candidate





## 57. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-finite-discrete-bijection；資料={"n":5,"map":[0,2,1,3,4]}。請依 [vertex_count, map, forward_continuous, inverse_continuous, homeomorphism, boundary] 欄序回答。

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

Wave5第五層核對=(5, [0, 2, 1, 3, 4], 是, 是, 是, finite_discrete_scope_only)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0057/)

同胚 · qf-mod36-homeo-finite-discrete-bijection · candidate





## 58. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-finite-discrete-bijection；資料={"n":5,"map":[0,2,1,4,3]}。請依 [vertex_count, map, forward_continuous, inverse_continuous, homeomorphism, boundary] 欄序回答。

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

Wave5第五層核對=(5, [0, 2, 1, 4, 3], 是, 是, 是, finite_discrete_scope_only)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0058/)

同胚 · qf-mod36-homeo-finite-discrete-bijection · candidate





## 59. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-finite-discrete-bijection；資料={"n":5,"map":[0,2,3,1,4]}。請依 [vertex_count, map, forward_continuous, inverse_continuous, homeomorphism, boundary] 欄序回答。

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

Wave5第五層核對=(5, [0, 2, 3, 1, 4], 是, 是, 是, finite_discrete_scope_only)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0059/)

同胚 · qf-mod36-homeo-finite-discrete-bijection · candidate





## 60. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-finite-discrete-bijection；資料={"n":5,"map":[0,2,3,4,1]}。請依 [vertex_count, map, forward_continuous, inverse_continuous, homeomorphism, boundary] 欄序回答。

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

Wave5第五層核對=(5, [0, 2, 3, 4, 1], 是, 是, 是, finite_discrete_scope_only)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0060/)

同胚 · qf-mod36-homeo-finite-discrete-bijection · candidate





## 61. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-finite-discrete-bijection；資料={"n":5,"map":[0,2,4,1,3]}。請依 [vertex_count, map, forward_continuous, inverse_continuous, homeomorphism, boundary] 欄序回答。

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

Wave5第五層核對=(5, [0, 2, 4, 1, 3], 是, 是, 是, finite_discrete_scope_only)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0061/)

同胚 · qf-mod36-homeo-finite-discrete-bijection · candidate





## 62. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-finite-discrete-bijection；資料={"n":5,"map":[0,2,4,3,1]}。請依 [vertex_count, map, forward_continuous, inverse_continuous, homeomorphism, boundary] 欄序回答。

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

Wave5第五層核對=(5, [0, 2, 4, 3, 1], 是, 是, 是, finite_discrete_scope_only)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0062/)

同胚 · qf-mod36-homeo-finite-discrete-bijection · candidate





## 63. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-finite-discrete-bijection；資料={"n":5,"map":[0,3,1,2,4]}。請依 [vertex_count, map, forward_continuous, inverse_continuous, homeomorphism, boundary] 欄序回答。

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

Wave5第五層核對=(5, [0, 3, 1, 2, 4], 是, 是, 是, finite_discrete_scope_only)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0063/)

同胚 · qf-mod36-homeo-finite-discrete-bijection · candidate





## 64. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-finite-discrete-bijection；資料={"n":5,"map":[0,3,1,4,2]}。請依 [vertex_count, map, forward_continuous, inverse_continuous, homeomorphism, boundary] 欄序回答。

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

Wave5第五層核對=(5, [0, 3, 1, 4, 2], 是, 是, 是, finite_discrete_scope_only)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0064/)

同胚 · qf-mod36-homeo-finite-discrete-bijection · candidate





## 65. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-finite-discrete-bijection；資料={"n":5,"map":[0,3,2,1,4]}。請依 [vertex_count, map, forward_continuous, inverse_continuous, homeomorphism, boundary] 欄序回答。

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

Wave5第五層核對=(5, [0, 3, 2, 1, 4], 是, 是, 是, finite_discrete_scope_only)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0065/)

同胚 · qf-mod36-homeo-finite-discrete-bijection · candidate





## 66. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-finite-discrete-bijection；資料={"n":5,"map":[0,3,2,4,1]}。請依 [vertex_count, map, forward_continuous, inverse_continuous, homeomorphism, boundary] 欄序回答。

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

Wave5第五層核對=(5, [0, 3, 2, 4, 1], 是, 是, 是, finite_discrete_scope_only)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0066/)

同胚 · qf-mod36-homeo-finite-discrete-bijection · candidate





## 67. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-finite-discrete-bijection；資料={"n":5,"map":[0,3,4,1,2]}。請依 [vertex_count, map, forward_continuous, inverse_continuous, homeomorphism, boundary] 欄序回答。

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

Wave5第五層核對=(5, [0, 3, 4, 1, 2], 是, 是, 是, finite_discrete_scope_only)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0067/)

同胚 · qf-mod36-homeo-finite-discrete-bijection · candidate





## 68. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-finite-discrete-bijection；資料={"n":5,"map":[0,3,4,2,1]}。請依 [vertex_count, map, forward_continuous, inverse_continuous, homeomorphism, boundary] 欄序回答。

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

Wave5第五層核對=(5, [0, 3, 4, 2, 1], 是, 是, 是, finite_discrete_scope_only)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0068/)

同胚 · qf-mod36-homeo-finite-discrete-bijection · candidate





## 69. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-finite-discrete-bijection；資料={"n":5,"map":[0,4,1,2,3]}。請依 [vertex_count, map, forward_continuous, inverse_continuous, homeomorphism, boundary] 欄序回答。

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

Wave5第五層核對=(5, [0, 4, 1, 2, 3], 是, 是, 是, finite_discrete_scope_only)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0069/)

同胚 · qf-mod36-homeo-finite-discrete-bijection · candidate





## 70. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-finite-discrete-bijection；資料={"n":5,"map":[0,4,1,3,2]}。請依 [vertex_count, map, forward_continuous, inverse_continuous, homeomorphism, boundary] 欄序回答。

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

Wave5第五層核對=(5, [0, 4, 1, 3, 2], 是, 是, 是, finite_discrete_scope_only)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0070/)

同胚 · qf-mod36-homeo-finite-discrete-bijection · candidate





## 71. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-finite-discrete-bijection；資料={"n":5,"map":[0,4,2,1,3]}。請依 [vertex_count, map, forward_continuous, inverse_continuous, homeomorphism, boundary] 欄序回答。

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

Wave5第五層核對=(5, [0, 4, 2, 1, 3], 是, 是, 是, finite_discrete_scope_only)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0071/)

同胚 · qf-mod36-homeo-finite-discrete-bijection · candidate





## 72. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-finite-discrete-bijection；資料={"n":5,"map":[0,4,2,3,1]}。請依 [vertex_count, map, forward_continuous, inverse_continuous, homeomorphism, boundary] 欄序回答。

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

Wave5第五層核對=(5, [0, 4, 2, 3, 1], 是, 是, 是, finite_discrete_scope_only)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0072/)

同胚 · qf-mod36-homeo-finite-discrete-bijection · candidate





## 73. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-finite-discrete-bijection；資料={"n":5,"map":[0,4,3,1,2]}。請依 [vertex_count, map, forward_continuous, inverse_continuous, homeomorphism, boundary] 欄序回答。

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

Wave5第五層核對=(5, [0, 4, 3, 1, 2], 是, 是, 是, finite_discrete_scope_only)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0073/)

同胚 · qf-mod36-homeo-finite-discrete-bijection · candidate





## 74. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-finite-discrete-bijection；資料={"n":5,"map":[0,4,3,2,1]}。請依 [vertex_count, map, forward_continuous, inverse_continuous, homeomorphism, boundary] 欄序回答。

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

Wave5第五層核對=(5, [0, 4, 3, 2, 1], 是, 是, 是, finite_discrete_scope_only)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0074/)

同胚 · qf-mod36-homeo-finite-discrete-bijection · candidate





## 75. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-finite-discrete-bijection；資料={"n":5,"map":[1,0,2,3,4]}。請依 [vertex_count, map, forward_continuous, inverse_continuous, homeomorphism, boundary] 欄序回答。

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

Wave5第五層核對=(5, [1, 0, 2, 3, 4], 是, 是, 是, finite_discrete_scope_only)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0075/)

同胚 · qf-mod36-homeo-finite-discrete-bijection · candidate





## 76. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-metric-nonimplication；資料={"n":5,"map":[0,1,2,3,4],"source_scale":1,"target_scale":2}。請依 [vertex_count, homeomorphic, equal_scale_parameters, source_scale, target_scale, boundary] 欄序回答。

第三欄只比較兩個尺度參數；單點空間的等距性不由這一欄的否來否證。

查看答案與解釋(5, 是, 否, 1, 2, homeomorphism_does_not_imply_isometry_diffeomorphism_or_congruence)

Wave5第五層核對=(5, 是, 否, 1, 2, homeomorphism_does_not_imply_isometry_diffeomorphism_or_congruence)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0076/)

同胚 · qf-mod36-homeo-metric-nonimplication · candidate





## 77. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-metric-nonimplication；資料={"n":5,"map":[0,1,2,4,3],"source_scale":2,"target_scale":3}。請依 [vertex_count, homeomorphic, equal_scale_parameters, source_scale, target_scale, boundary] 欄序回答。

第三欄只比較兩個尺度參數；單點空間的等距性不由這一欄的否來否證。

查看答案與解釋(5, 是, 否, 2, 3, homeomorphism_does_not_imply_isometry_diffeomorphism_or_congruence)

Wave5第五層核對=(5, 是, 否, 2, 3, homeomorphism_does_not_imply_isometry_diffeomorphism_or_congruence)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0077/)

同胚 · qf-mod36-homeo-metric-nonimplication · candidate





## 78. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-metric-nonimplication；資料={"n":5,"map":[0,1,3,2,4],"source_scale":3,"target_scale":4}。請依 [vertex_count, homeomorphic, equal_scale_parameters, source_scale, target_scale, boundary] 欄序回答。

第三欄只比較兩個尺度參數；單點空間的等距性不由這一欄的否來否證。

查看答案與解釋(5, 是, 否, 3, 4, homeomorphism_does_not_imply_isometry_diffeomorphism_or_congruence)

Wave5第五層核對=(5, 是, 否, 3, 4, homeomorphism_does_not_imply_isometry_diffeomorphism_or_congruence)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0078/)

同胚 · qf-mod36-homeo-metric-nonimplication · candidate





## 79. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-metric-nonimplication；資料={"n":5,"map":[0,1,3,4,2],"source_scale":4,"target_scale":5}。請依 [vertex_count, homeomorphic, equal_scale_parameters, source_scale, target_scale, boundary] 欄序回答。

第三欄只比較兩個尺度參數；單點空間的等距性不由這一欄的否來否證。

查看答案與解釋(5, 是, 否, 4, 5, homeomorphism_does_not_imply_isometry_diffeomorphism_or_congruence)

Wave5第五層核對=(5, 是, 否, 4, 5, homeomorphism_does_not_imply_isometry_diffeomorphism_or_congruence)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0079/)

同胚 · qf-mod36-homeo-metric-nonimplication · candidate





## 80. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-metric-nonimplication；資料={"n":5,"map":[0,1,4,2,3],"source_scale":5,"target_scale":6}。請依 [vertex_count, homeomorphic, equal_scale_parameters, source_scale, target_scale, boundary] 欄序回答。

第三欄只比較兩個尺度參數；單點空間的等距性不由這一欄的否來否證。

查看答案與解釋(5, 是, 否, 5, 6, homeomorphism_does_not_imply_isometry_diffeomorphism_or_congruence)

Wave5第五層核對=(5, 是, 否, 5, 6, homeomorphism_does_not_imply_isometry_diffeomorphism_or_congruence)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0080/)

同胚 · qf-mod36-homeo-metric-nonimplication · candidate





## 81. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-metric-nonimplication；資料={"n":5,"map":[0,1,4,3,2],"source_scale":6,"target_scale":7}。請依 [vertex_count, homeomorphic, equal_scale_parameters, source_scale, target_scale, boundary] 欄序回答。

第三欄只比較兩個尺度參數；單點空間的等距性不由這一欄的否來否證。

查看答案與解釋(5, 是, 否, 6, 7, homeomorphism_does_not_imply_isometry_diffeomorphism_or_congruence)

Wave5第五層核對=(5, 是, 否, 6, 7, homeomorphism_does_not_imply_isometry_diffeomorphism_or_congruence)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0081/)

同胚 · qf-mod36-homeo-metric-nonimplication · candidate





## 82. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-metric-nonimplication；資料={"n":5,"map":[0,2,1,3,4],"source_scale":7,"target_scale":8}。請依 [vertex_count, homeomorphic, equal_scale_parameters, source_scale, target_scale, boundary] 欄序回答。

第三欄只比較兩個尺度參數；單點空間的等距性不由這一欄的否來否證。

查看答案與解釋(5, 是, 否, 7, 8, homeomorphism_does_not_imply_isometry_diffeomorphism_or_congruence)

Wave5第五層核對=(5, 是, 否, 7, 8, homeomorphism_does_not_imply_isometry_diffeomorphism_or_congruence)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0082/)

同胚 · qf-mod36-homeo-metric-nonimplication · candidate





## 83. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-metric-nonimplication；資料={"n":5,"map":[0,2,1,4,3],"source_scale":8,"target_scale":9}。請依 [vertex_count, homeomorphic, equal_scale_parameters, source_scale, target_scale, boundary] 欄序回答。

第三欄只比較兩個尺度參數；單點空間的等距性不由這一欄的否來否證。

查看答案與解釋(5, 是, 否, 8, 9, homeomorphism_does_not_imply_isometry_diffeomorphism_or_congruence)

Wave5第五層核對=(5, 是, 否, 8, 9, homeomorphism_does_not_imply_isometry_diffeomorphism_or_congruence)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0083/)

同胚 · qf-mod36-homeo-metric-nonimplication · candidate





## 84. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-metric-nonimplication；資料={"n":5,"map":[0,2,3,1,4],"source_scale":9,"target_scale":10}。請依 [vertex_count, homeomorphic, equal_scale_parameters, source_scale, target_scale, boundary] 欄序回答。

第三欄只比較兩個尺度參數；單點空間的等距性不由這一欄的否來否證。

查看答案與解釋(5, 是, 否, 9, 10, homeomorphism_does_not_imply_isometry_diffeomorphism_or_congruence)

Wave5第五層核對=(5, 是, 否, 9, 10, homeomorphism_does_not_imply_isometry_diffeomorphism_or_congruence)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0084/)

同胚 · qf-mod36-homeo-metric-nonimplication · candidate





## 85. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-metric-nonimplication；資料={"n":5,"map":[0,2,3,4,1],"source_scale":10,"target_scale":11}。請依 [vertex_count, homeomorphic, equal_scale_parameters, source_scale, target_scale, boundary] 欄序回答。

第三欄只比較兩個尺度參數；單點空間的等距性不由這一欄的否來否證。

查看答案與解釋(5, 是, 否, 10, 11, homeomorphism_does_not_imply_isometry_diffeomorphism_or_congruence)

Wave5第五層核對=(5, 是, 否, 10, 11, homeomorphism_does_not_imply_isometry_diffeomorphism_or_congruence)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0085/)

同胚 · qf-mod36-homeo-metric-nonimplication · candidate





## 86. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-metric-nonimplication；資料={"n":5,"map":[0,2,4,1,3],"source_scale":11,"target_scale":12}。請依 [vertex_count, homeomorphic, equal_scale_parameters, source_scale, target_scale, boundary] 欄序回答。

第三欄只比較兩個尺度參數；單點空間的等距性不由這一欄的否來否證。

查看答案與解釋(5, 是, 否, 11, 12, homeomorphism_does_not_imply_isometry_diffeomorphism_or_congruence)

Wave5第五層核對=(5, 是, 否, 11, 12, homeomorphism_does_not_imply_isometry_diffeomorphism_or_congruence)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0086/)

同胚 · qf-mod36-homeo-metric-nonimplication · candidate





## 87. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-metric-nonimplication；資料={"n":5,"map":[0,2,4,3,1],"source_scale":12,"target_scale":13}。請依 [vertex_count, homeomorphic, equal_scale_parameters, source_scale, target_scale, boundary] 欄序回答。

第三欄只比較兩個尺度參數；單點空間的等距性不由這一欄的否來否證。

查看答案與解釋(5, 是, 否, 12, 13, homeomorphism_does_not_imply_isometry_diffeomorphism_or_congruence)

Wave5第五層核對=(5, 是, 否, 12, 13, homeomorphism_does_not_imply_isometry_diffeomorphism_or_congruence)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0087/)

同胚 · qf-mod36-homeo-metric-nonimplication · candidate





## 88. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-metric-nonimplication；資料={"n":5,"map":[0,3,1,2,4],"source_scale":13,"target_scale":14}。請依 [vertex_count, homeomorphic, equal_scale_parameters, source_scale, target_scale, boundary] 欄序回答。

第三欄只比較兩個尺度參數；單點空間的等距性不由這一欄的否來否證。

查看答案與解釋(5, 是, 否, 13, 14, homeomorphism_does_not_imply_isometry_diffeomorphism_or_congruence)

Wave5第五層核對=(5, 是, 否, 13, 14, homeomorphism_does_not_imply_isometry_diffeomorphism_or_congruence)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0088/)

同胚 · qf-mod36-homeo-metric-nonimplication · candidate





## 89. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-metric-nonimplication；資料={"n":5,"map":[0,3,1,4,2],"source_scale":14,"target_scale":15}。請依 [vertex_count, homeomorphic, equal_scale_parameters, source_scale, target_scale, boundary] 欄序回答。

第三欄只比較兩個尺度參數；單點空間的等距性不由這一欄的否來否證。

查看答案與解釋(5, 是, 否, 14, 15, homeomorphism_does_not_imply_isometry_diffeomorphism_or_congruence)

Wave5第五層核對=(5, 是, 否, 14, 15, homeomorphism_does_not_imply_isometry_diffeomorphism_or_congruence)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0089/)

同胚 · qf-mod36-homeo-metric-nonimplication · candidate





## 90. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-metric-nonimplication；資料={"n":5,"map":[0,3,2,1,4],"source_scale":15,"target_scale":16}。請依 [vertex_count, homeomorphic, equal_scale_parameters, source_scale, target_scale, boundary] 欄序回答。

第三欄只比較兩個尺度參數；單點空間的等距性不由這一欄的否來否證。

查看答案與解釋(5, 是, 否, 15, 16, homeomorphism_does_not_imply_isometry_diffeomorphism_or_congruence)

Wave5第五層核對=(5, 是, 否, 15, 16, homeomorphism_does_not_imply_isometry_diffeomorphism_or_congruence)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0090/)

同胚 · qf-mod36-homeo-metric-nonimplication · candidate





## 91. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-metric-nonimplication；資料={"n":5,"map":[0,3,2,4,1],"source_scale":16,"target_scale":17}。請依 [vertex_count, homeomorphic, equal_scale_parameters, source_scale, target_scale, boundary] 欄序回答。

第三欄只比較兩個尺度參數；單點空間的等距性不由這一欄的否來否證。

查看答案與解釋(5, 是, 否, 16, 17, homeomorphism_does_not_imply_isometry_diffeomorphism_or_congruence)

Wave5第五層核對=(5, 是, 否, 16, 17, homeomorphism_does_not_imply_isometry_diffeomorphism_or_congruence)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0091/)

同胚 · qf-mod36-homeo-metric-nonimplication · candidate





## 92. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-metric-nonimplication；資料={"n":5,"map":[0,3,4,1,2],"source_scale":17,"target_scale":18}。請依 [vertex_count, homeomorphic, equal_scale_parameters, source_scale, target_scale, boundary] 欄序回答。

第三欄只比較兩個尺度參數；單點空間的等距性不由這一欄的否來否證。

查看答案與解釋(5, 是, 否, 17, 18, homeomorphism_does_not_imply_isometry_diffeomorphism_or_congruence)

Wave5第五層核對=(5, 是, 否, 17, 18, homeomorphism_does_not_imply_isometry_diffeomorphism_or_congruence)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0092/)

同胚 · qf-mod36-homeo-metric-nonimplication · candidate





## 93. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-metric-nonimplication；資料={"n":5,"map":[0,3,4,2,1],"source_scale":18,"target_scale":19}。請依 [vertex_count, homeomorphic, equal_scale_parameters, source_scale, target_scale, boundary] 欄序回答。

第三欄只比較兩個尺度參數；單點空間的等距性不由這一欄的否來否證。

查看答案與解釋(5, 是, 否, 18, 19, homeomorphism_does_not_imply_isometry_diffeomorphism_or_congruence)

Wave5第五層核對=(5, 是, 否, 18, 19, homeomorphism_does_not_imply_isometry_diffeomorphism_or_congruence)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0093/)

同胚 · qf-mod36-homeo-metric-nonimplication · candidate





## 94. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-metric-nonimplication；資料={"n":5,"map":[0,4,1,2,3],"source_scale":19,"target_scale":20}。請依 [vertex_count, homeomorphic, equal_scale_parameters, source_scale, target_scale, boundary] 欄序回答。

第三欄只比較兩個尺度參數；單點空間的等距性不由這一欄的否來否證。

查看答案與解釋(5, 是, 否, 19, 20, homeomorphism_does_not_imply_isometry_diffeomorphism_or_congruence)

Wave5第五層核對=(5, 是, 否, 19, 20, homeomorphism_does_not_imply_isometry_diffeomorphism_or_congruence)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0094/)

同胚 · qf-mod36-homeo-metric-nonimplication · candidate





## 95. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-metric-nonimplication；資料={"n":5,"map":[0,4,1,3,2],"source_scale":20,"target_scale":21}。請依 [vertex_count, homeomorphic, equal_scale_parameters, source_scale, target_scale, boundary] 欄序回答。

第三欄只比較兩個尺度參數；單點空間的等距性不由這一欄的否來否證。

查看答案與解釋(5, 是, 否, 20, 21, homeomorphism_does_not_imply_isometry_diffeomorphism_or_congruence)

Wave5第五層核對=(5, 是, 否, 20, 21, homeomorphism_does_not_imply_isometry_diffeomorphism_or_congruence)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0095/)

同胚 · qf-mod36-homeo-metric-nonimplication · candidate





## 96. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-metric-nonimplication；資料={"n":5,"map":[0,4,2,1,3],"source_scale":21,"target_scale":22}。請依 [vertex_count, homeomorphic, equal_scale_parameters, source_scale, target_scale, boundary] 欄序回答。

第三欄只比較兩個尺度參數；單點空間的等距性不由這一欄的否來否證。

查看答案與解釋(5, 是, 否, 21, 22, homeomorphism_does_not_imply_isometry_diffeomorphism_or_congruence)

Wave5第五層核對=(5, 是, 否, 21, 22, homeomorphism_does_not_imply_isometry_diffeomorphism_or_congruence)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0096/)

同胚 · qf-mod36-homeo-metric-nonimplication · candidate





## 97. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-metric-nonimplication；資料={"n":5,"map":[0,4,2,3,1],"source_scale":22,"target_scale":23}。請依 [vertex_count, homeomorphic, equal_scale_parameters, source_scale, target_scale, boundary] 欄序回答。

第三欄只比較兩個尺度參數；單點空間的等距性不由這一欄的否來否證。

查看答案與解釋(5, 是, 否, 22, 23, homeomorphism_does_not_imply_isometry_diffeomorphism_or_congruence)

Wave5第五層核對=(5, 是, 否, 22, 23, homeomorphism_does_not_imply_isometry_diffeomorphism_or_congruence)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0097/)

同胚 · qf-mod36-homeo-metric-nonimplication · candidate





## 98. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-metric-nonimplication；資料={"n":5,"map":[0,4,3,1,2],"source_scale":23,"target_scale":24}。請依 [vertex_count, homeomorphic, equal_scale_parameters, source_scale, target_scale, boundary] 欄序回答。

第三欄只比較兩個尺度參數；單點空間的等距性不由這一欄的否來否證。

查看答案與解釋(5, 是, 否, 23, 24, homeomorphism_does_not_imply_isometry_diffeomorphism_or_congruence)

Wave5第五層核對=(5, 是, 否, 23, 24, homeomorphism_does_not_imply_isometry_diffeomorphism_or_congruence)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0098/)

同胚 · qf-mod36-homeo-metric-nonimplication · candidate





## 99. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-metric-nonimplication；資料={"n":5,"map":[0,4,3,2,1],"source_scale":24,"target_scale":25}。請依 [vertex_count, homeomorphic, equal_scale_parameters, source_scale, target_scale, boundary] 欄序回答。

第三欄只比較兩個尺度參數；單點空間的等距性不由這一欄的否來否證。

查看答案與解釋(5, 是, 否, 24, 25, homeomorphism_does_not_imply_isometry_diffeomorphism_or_congruence)

Wave5第五層核對=(5, 是, 否, 24, 25, homeomorphism_does_not_imply_isometry_diffeomorphism_or_congruence)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0099/)

同胚 · qf-mod36-homeo-metric-nonimplication · candidate





## 100. 同胚

完整有限來源與目標拓撲、雙射及全部開集逆像。操作=homeo-metric-nonimplication；資料={"n":5,"map":[1,0,2,3,4],"source_scale":25,"target_scale":26}。請依 [vertex_count, homeomorphic, equal_scale_parameters, source_scale, target_scale, boundary] 欄序回答。

第三欄只比較兩個尺度參數；單點空間的等距性不由這一欄的否來否證。

查看答案與解釋(5, 是, 否, 25, 26, homeomorphism_does_not_imply_isometry_diffeomorphism_or_congruence)

Wave5第五層核對=(5, 是, 否, 25, 26, homeomorphism_does_not_imply_isometry_diffeomorphism_or_congruence)；依完整明示資料獨立重算；homeomorphism同時要求f連續及逆映射連續；一般continuous bijection不足；有限離散雙射結論不得外推，也不推出等距、可微或幾何全等。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r05-homeomorphism-0100/)

同胚 · qf-mod36-homeo-metric-nonimplication · candidate



[原始題目 JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261014-advance-20261105-r05-homeomorphism-foundations/questions.jsonl) · [驗收報告](https://ocme.evemisslab.com/data/questions/batches/batch-20261014-advance-20261105-r05-homeomorphism-foundations/validation-report.json)