# 鄰域基礎 · 脈衝 R02

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-20261013-advance-20261019-r02-neighborhood-foundations · 2026-10-13 · 100 題



## 1. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-witness；資料={"n":4,"opens":[[],[0],[0,1],[0,1,2],[0,1,2,3]],"x":0,"candidate":[0,1]}。請依 [n,x,point_qualified,candidate,open_witnesses_or_不求值,neighborhood_or_不求值] 欄序回答。

查看答案與解釋(4, 0, 是, [0, 1], [[0], [0, 1]], 是)

第二批擴展核對=(4, 0, 是, [0, 1], [[0], [0, 1]], 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0001/)

鄰域 · qf-ext19-neighborhood-witness · candidate





## 2. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-witness；資料={"n":4,"opens":[[],[1],[0,1],[0,1,2],[0,1,2,3]],"x":1,"candidate":[2]}。請依 [n,x,point_qualified,candidate,open_witnesses_or_不求值,neighborhood_or_不求值] 欄序回答。

查看答案與解釋(4, 1, 是, [2], [], 否)

第二批擴展核對=(4, 1, 是, [2], [], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0002/)

鄰域 · qf-ext19-neighborhood-witness · candidate





## 3. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-witness；資料={"n":4,"opens":[[],[2],[0,2],[0,1,2],[0,1,2,3]],"x":2,"candidate":[0,2]}。請依 [n,x,point_qualified,candidate,open_witnesses_or_不求值,neighborhood_or_不求值] 欄序回答。

查看答案與解釋(4, 2, 是, [0, 2], [[2], [0, 2]], 是)

第二批擴展核對=(4, 2, 是, [0, 2], [[2], [0, 2]], 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0003/)

鄰域 · qf-ext19-neighborhood-witness · candidate





## 4. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-witness；資料={"n":4,"opens":[[],[3],[0,3],[0,1,3],[0,1,2,3]],"x":3,"candidate":[1,2]}。請依 [n,x,point_qualified,candidate,open_witnesses_or_不求值,neighborhood_or_不求值] 欄序回答。

查看答案與解釋(4, 3, 是, [1, 2], [], 否)

第二批擴展核對=(4, 3, 是, [1, 2], [], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0004/)

鄰域 · qf-ext19-neighborhood-witness · candidate





## 5. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-witness；資料={"n":4,"opens":[[],[0],[0,2],[0,1,2],[0,1,2,3]],"x":-1,"candidate":[0,1,2]}。請依 [n,x,point_qualified,candidate,open_witnesses_or_不求值,neighborhood_or_不求值] 欄序回答。

查看答案與解釋(4, -1, 否, [0, 1, 2], 不求值, 不求值)

第二批擴展核對=(4, -1, 否, [0, 1, 2], 不求值, 不求值)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0005/)

鄰域 · qf-ext19-neighborhood-witness · candidate





## 6. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-witness；資料={"n":4,"opens":[[],[1],[1,2],[0,1,2],[0,1,2,3]],"x":1,"candidate":[3]}。請依 [n,x,point_qualified,candidate,open_witnesses_or_不求值,neighborhood_or_不求值] 欄序回答。

查看答案與解釋(4, 1, 是, [3], [], 否)

第二批擴展核對=(4, 1, 是, [3], [], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0006/)

鄰域 · qf-ext19-neighborhood-witness · candidate





## 7. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-witness；資料={"n":4,"opens":[[],[2],[1,2],[0,1,2],[0,1,2,3]],"x":2,"candidate":[0,3]}。請依 [n,x,point_qualified,candidate,open_witnesses_or_不求值,neighborhood_or_不求值] 欄序回答。

查看答案與解釋(4, 2, 是, [0, 3], [], 否)

第二批擴展核對=(4, 2, 是, [0, 3], [], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0007/)

鄰域 · qf-ext19-neighborhood-witness · candidate





## 8. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-witness；資料={"n":4,"opens":[[],[3],[1,3],[0,1,3],[0,1,2,3]],"x":3,"candidate":[1,3]}。請依 [n,x,point_qualified,candidate,open_witnesses_or_不求值,neighborhood_or_不求值] 欄序回答。

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

第二批擴展核對=(4, 3, 是, [1, 3], [[3], [1, 3]], 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0008/)

鄰域 · qf-ext19-neighborhood-witness · candidate





## 9. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-witness；資料={"n":4,"opens":[[],[0],[0,3],[0,1,3],[0,1,2,3]],"x":0,"candidate":[0,1,3]}。請依 [n,x,point_qualified,candidate,open_witnesses_or_不求值,neighborhood_or_不求值] 欄序回答。

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

第二批擴展核對=(4, 0, 是, [0, 1, 3], [[0], [0, 3], [0, 1, 3]], 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0009/)

鄰域 · qf-ext19-neighborhood-witness · candidate





## 10. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-witness；資料={"n":4,"opens":[[],[1],[1,3],[0,1,3],[0,1,2,3]],"x":-1,"candidate":[2,3]}。請依 [n,x,point_qualified,candidate,open_witnesses_or_不求值,neighborhood_or_不求值] 欄序回答。

查看答案與解釋(4, -1, 否, [2, 3], 不求值, 不求值)

第二批擴展核對=(4, -1, 否, [2, 3], 不求值, 不求值)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0010/)

鄰域 · qf-ext19-neighborhood-witness · candidate





## 11. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-witness；資料={"n":4,"opens":[[],[2],[2,3],[0,2,3],[0,1,2,3]],"x":2,"candidate":[0,2,3]}。請依 [n,x,point_qualified,candidate,open_witnesses_or_不求值,neighborhood_or_不求值] 欄序回答。

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

第二批擴展核對=(4, 2, 是, [0, 2, 3], [[2], [2, 3], [0, 2, 3]], 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0011/)

鄰域 · qf-ext19-neighborhood-witness · candidate





## 12. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-witness；資料={"n":4,"opens":[[],[3],[2,3],[0,2,3],[0,1,2,3]],"x":3,"candidate":[1,2,3]}。請依 [n,x,point_qualified,candidate,open_witnesses_or_不求值,neighborhood_or_不求值] 欄序回答。

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

第二批擴展核對=(4, 3, 是, [1, 2, 3], [[3], [2, 3]], 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0012/)

鄰域 · qf-ext19-neighborhood-witness · candidate





## 13. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-witness；資料={"n":4,"opens":[[],[0],[0,1],[0,1,3],[0,1,2,3]],"x":0,"candidate":[0,1,2,3]}。請依 [n,x,point_qualified,candidate,open_witnesses_or_不求值,neighborhood_or_不求值] 欄序回答。

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

第二批擴展核對=(4, 0, 是, [0, 1, 2, 3], [[0], [0, 1], [0, 1, 3], [0, 1, 2, 3]], 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0013/)

鄰域 · qf-ext19-neighborhood-witness · candidate





## 14. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-witness；資料={"n":4,"opens":[[],[1],[0,1],[0,1,3],[0,1,2,3]],"x":1,"candidate":[]}。請依 [n,x,point_qualified,candidate,open_witnesses_or_不求值,neighborhood_or_不求值] 欄序回答。

查看答案與解釋(4, 1, 是, [], [], 否)

第二批擴展核對=(4, 1, 是, [], [], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0014/)

鄰域 · qf-ext19-neighborhood-witness · candidate





## 15. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-witness；資料={"n":4,"opens":[[],[2],[0,2],[0,2,3],[0,1,2,3]],"x":-1,"candidate":[0]}。請依 [n,x,point_qualified,candidate,open_witnesses_or_不求值,neighborhood_or_不求值] 欄序回答。

查看答案與解釋(4, -1, 否, [0], 不求值, 不求值)

第二批擴展核對=(4, -1, 否, [0], 不求值, 不求值)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0015/)

鄰域 · qf-ext19-neighborhood-witness · candidate





## 16. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-witness；資料={"n":4,"opens":[[],[3],[0,3],[0,2,3],[0,1,2,3]],"x":3,"candidate":[1]}。請依 [n,x,point_qualified,candidate,open_witnesses_or_不求值,neighborhood_or_不求值] 欄序回答。

查看答案與解釋(4, 3, 是, [1], [], 否)

第二批擴展核對=(4, 3, 是, [1], [], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0016/)

鄰域 · qf-ext19-neighborhood-witness · candidate





## 17. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-witness；資料={"n":4,"opens":[[],[0],[0,2],[0,2,3],[0,1,2,3]],"x":0,"candidate":[0,1]}。請依 [n,x,point_qualified,candidate,open_witnesses_or_不求值,neighborhood_or_不求值] 欄序回答。

查看答案與解釋(4, 0, 是, [0, 1], [[0]], 是)

第二批擴展核對=(4, 0, 是, [0, 1], [[0]], 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0017/)

鄰域 · qf-ext19-neighborhood-witness · candidate





## 18. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-witness；資料={"n":4,"opens":[[],[1],[1,2],[1,2,3],[0,1,2,3]],"x":1,"candidate":[2]}。請依 [n,x,point_qualified,candidate,open_witnesses_or_不求值,neighborhood_or_不求值] 欄序回答。

查看答案與解釋(4, 1, 是, [2], [], 否)

第二批擴展核對=(4, 1, 是, [2], [], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0018/)

鄰域 · qf-ext19-neighborhood-witness · candidate





## 19. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-witness；資料={"n":4,"opens":[[],[2],[1,2],[1,2,3],[0,1,2,3]],"x":2,"candidate":[0,2]}。請依 [n,x,point_qualified,candidate,open_witnesses_or_不求值,neighborhood_or_不求值] 欄序回答。

查看答案與解釋(4, 2, 是, [0, 2], [[2]], 是)

第二批擴展核對=(4, 2, 是, [0, 2], [[2]], 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0019/)

鄰域 · qf-ext19-neighborhood-witness · candidate





## 20. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-witness；資料={"n":4,"opens":[[],[3],[1,3],[1,2,3],[0,1,2,3]],"x":-1,"candidate":[1,2]}。請依 [n,x,point_qualified,candidate,open_witnesses_or_不求值,neighborhood_or_不求值] 欄序回答。

查看答案與解釋(4, -1, 否, [1, 2], 不求值, 不求值)

第二批擴展核對=(4, -1, 否, [1, 2], 不求值, 不求值)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0020/)

鄰域 · qf-ext19-neighborhood-witness · candidate





## 21. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-witness；資料={"n":4,"opens":[[],[0],[0,3],[0,2,3],[0,1,2,3]],"x":0,"candidate":[0,1,2]}。請依 [n,x,point_qualified,candidate,open_witnesses_or_不求值,neighborhood_or_不求值] 欄序回答。

查看答案與解釋(4, 0, 是, [0, 1, 2], [[0]], 是)

第二批擴展核對=(4, 0, 是, [0, 1, 2], [[0]], 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0021/)

鄰域 · qf-ext19-neighborhood-witness · candidate





## 22. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-witness；資料={"n":4,"opens":[[],[1],[1,3],[1,2,3],[0,1,2,3]],"x":1,"candidate":[3]}。請依 [n,x,point_qualified,candidate,open_witnesses_or_不求值,neighborhood_or_不求值] 欄序回答。

查看答案與解釋(4, 1, 是, [3], [], 否)

第二批擴展核對=(4, 1, 是, [3], [], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0022/)

鄰域 · qf-ext19-neighborhood-witness · candidate





## 23. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-witness；資料={"n":4,"opens":[[],[2],[2,3],[1,2,3],[0,1,2,3]],"x":2,"candidate":[0,3]}。請依 [n,x,point_qualified,candidate,open_witnesses_or_不求值,neighborhood_or_不求值] 欄序回答。

查看答案與解釋(4, 2, 是, [0, 3], [], 否)

第二批擴展核對=(4, 2, 是, [0, 3], [], 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0023/)

鄰域 · qf-ext19-neighborhood-witness · candidate





## 24. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-witness；資料={"n":4,"opens":[[],[3],[2,3],[1,2,3],[0,1,2,3]],"x":3,"candidate":[1,3]}。請依 [n,x,point_qualified,candidate,open_witnesses_or_不求值,neighborhood_or_不求值] 欄序回答。

查看答案與解釋(4, 3, 是, [1, 3], [[3]], 是)

第二批擴展核對=(4, 3, 是, [1, 3], [[3]], 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0024/)

鄰域 · qf-ext19-neighborhood-witness · candidate





## 25. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-witness；資料={"n":3,"opens":[[],[0],[0,1],[0,1,2]],"x":-1,"candidate":[0,1]}。請依 [n,x,point_qualified,candidate,open_witnesses_or_不求值,neighborhood_or_不求值] 欄序回答。

查看答案與解釋(3, -1, 否, [0, 1], 不求值, 不求值)

第二批擴展核對=(3, -1, 否, [0, 1], 不求值, 不求值)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0025/)

鄰域 · qf-ext19-neighborhood-witness · candidate





## 26. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-qualification；資料={"n":4,"opens":[[],[0],[0,1],[0,1,2],[0,1,2,3]],"x":0,"candidate":[0,1]}。請依 [n,x,point_qualified,candidate,x_in_candidate,candidate_open,neighborhood] 欄序回答。

查看答案與解釋(4, 0, 是, [0, 1], 是, 是, 是)

第二批擴展核對=(4, 0, 是, [0, 1], 是, 是, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0026/)

鄰域 · qf-ext19-neighborhood-qualification · candidate





## 27. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-qualification；資料={"n":4,"opens":[[],[1],[0,1],[0,1,2],[0,1,2,3]],"x":1,"candidate":[2]}。請依 [n,x,point_qualified,candidate,x_in_candidate,candidate_open,neighborhood] 欄序回答。

查看答案與解釋(4, 1, 是, [2], 否, 否, 否)

第二批擴展核對=(4, 1, 是, [2], 否, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0027/)

鄰域 · qf-ext19-neighborhood-qualification · candidate





## 28. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-qualification；資料={"n":4,"opens":[[],[2],[0,2],[0,1,2],[0,1,2,3]],"x":2,"candidate":[0,2]}。請依 [n,x,point_qualified,candidate,x_in_candidate,candidate_open,neighborhood] 欄序回答。

查看答案與解釋(4, 2, 是, [0, 2], 是, 是, 是)

第二批擴展核對=(4, 2, 是, [0, 2], 是, 是, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0028/)

鄰域 · qf-ext19-neighborhood-qualification · candidate





## 29. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-qualification；資料={"n":4,"opens":[[],[3],[0,3],[0,1,3],[0,1,2,3]],"x":3,"candidate":[1,2]}。請依 [n,x,point_qualified,candidate,x_in_candidate,candidate_open,neighborhood] 欄序回答。

查看答案與解釋(4, 3, 是, [1, 2], 否, 否, 否)

第二批擴展核對=(4, 3, 是, [1, 2], 否, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0029/)

鄰域 · qf-ext19-neighborhood-qualification · candidate





## 30. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-qualification；資料={"n":4,"opens":[[],[0],[0,2],[0,1,2],[0,1,2,3]],"x":-1,"candidate":[0,1,2]}。請依 [n,x,point_qualified,candidate,x_in_candidate,candidate_open,neighborhood] 欄序回答。

查看答案與解釋(4, -1, 否, [0, 1, 2], 不求值, 不求值, 不求值)

第二批擴展核對=(4, -1, 否, [0, 1, 2], 不求值, 不求值, 不求值)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0030/)

鄰域 · qf-ext19-neighborhood-qualification · candidate





## 31. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-qualification；資料={"n":4,"opens":[[],[1],[1,2],[0,1,2],[0,1,2,3]],"x":1,"candidate":[3]}。請依 [n,x,point_qualified,candidate,x_in_candidate,candidate_open,neighborhood] 欄序回答。

查看答案與解釋(4, 1, 是, [3], 否, 否, 否)

第二批擴展核對=(4, 1, 是, [3], 否, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0031/)

鄰域 · qf-ext19-neighborhood-qualification · candidate





## 32. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-qualification；資料={"n":4,"opens":[[],[2],[1,2],[0,1,2],[0,1,2,3]],"x":2,"candidate":[0,3]}。請依 [n,x,point_qualified,candidate,x_in_candidate,candidate_open,neighborhood] 欄序回答。

查看答案與解釋(4, 2, 是, [0, 3], 否, 否, 否)

第二批擴展核對=(4, 2, 是, [0, 3], 否, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0032/)

鄰域 · qf-ext19-neighborhood-qualification · candidate





## 33. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-qualification；資料={"n":4,"opens":[[],[3],[1,3],[0,1,3],[0,1,2,3]],"x":3,"candidate":[1,3]}。請依 [n,x,point_qualified,candidate,x_in_candidate,candidate_open,neighborhood] 欄序回答。

查看答案與解釋(4, 3, 是, [1, 3], 是, 是, 是)

第二批擴展核對=(4, 3, 是, [1, 3], 是, 是, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0033/)

鄰域 · qf-ext19-neighborhood-qualification · candidate





## 34. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-qualification；資料={"n":4,"opens":[[],[0],[0,3],[0,1,3],[0,1,2,3]],"x":0,"candidate":[0,1,3]}。請依 [n,x,point_qualified,candidate,x_in_candidate,candidate_open,neighborhood] 欄序回答。

查看答案與解釋(4, 0, 是, [0, 1, 3], 是, 是, 是)

第二批擴展核對=(4, 0, 是, [0, 1, 3], 是, 是, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0034/)

鄰域 · qf-ext19-neighborhood-qualification · candidate





## 35. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-qualification；資料={"n":4,"opens":[[],[1],[1,3],[0,1,3],[0,1,2,3]],"x":-1,"candidate":[2,3]}。請依 [n,x,point_qualified,candidate,x_in_candidate,candidate_open,neighborhood] 欄序回答。

查看答案與解釋(4, -1, 否, [2, 3], 不求值, 不求值, 不求值)

第二批擴展核對=(4, -1, 否, [2, 3], 不求值, 不求值, 不求值)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0035/)

鄰域 · qf-ext19-neighborhood-qualification · candidate





## 36. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-qualification；資料={"n":4,"opens":[[],[2],[2,3],[0,2,3],[0,1,2,3]],"x":2,"candidate":[0,2,3]}。請依 [n,x,point_qualified,candidate,x_in_candidate,candidate_open,neighborhood] 欄序回答。

查看答案與解釋(4, 2, 是, [0, 2, 3], 是, 是, 是)

第二批擴展核對=(4, 2, 是, [0, 2, 3], 是, 是, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0036/)

鄰域 · qf-ext19-neighborhood-qualification · candidate





## 37. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-qualification；資料={"n":4,"opens":[[],[3],[2,3],[0,2,3],[0,1,2,3]],"x":3,"candidate":[1,2,3]}。請依 [n,x,point_qualified,candidate,x_in_candidate,candidate_open,neighborhood] 欄序回答。

查看答案與解釋(4, 3, 是, [1, 2, 3], 是, 否, 是)

第二批擴展核對=(4, 3, 是, [1, 2, 3], 是, 否, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0037/)

鄰域 · qf-ext19-neighborhood-qualification · candidate





## 38. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-qualification；資料={"n":4,"opens":[[],[0],[0,1],[0,1,3],[0,1,2,3]],"x":0,"candidate":[0,1,2,3]}。請依 [n,x,point_qualified,candidate,x_in_candidate,candidate_open,neighborhood] 欄序回答。

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

第二批擴展核對=(4, 0, 是, [0, 1, 2, 3], 是, 是, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0038/)

鄰域 · qf-ext19-neighborhood-qualification · candidate





## 39. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-qualification；資料={"n":4,"opens":[[],[1],[0,1],[0,1,3],[0,1,2,3]],"x":1,"candidate":[]}。請依 [n,x,point_qualified,candidate,x_in_candidate,candidate_open,neighborhood] 欄序回答。

查看答案與解釋(4, 1, 是, [], 否, 是, 否)

第二批擴展核對=(4, 1, 是, [], 否, 是, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0039/)

鄰域 · qf-ext19-neighborhood-qualification · candidate





## 40. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-qualification；資料={"n":4,"opens":[[],[2],[0,2],[0,2,3],[0,1,2,3]],"x":-1,"candidate":[0]}。請依 [n,x,point_qualified,candidate,x_in_candidate,candidate_open,neighborhood] 欄序回答。

查看答案與解釋(4, -1, 否, [0], 不求值, 不求值, 不求值)

第二批擴展核對=(4, -1, 否, [0], 不求值, 不求值, 不求值)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0040/)

鄰域 · qf-ext19-neighborhood-qualification · candidate





## 41. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-qualification；資料={"n":4,"opens":[[],[3],[0,3],[0,2,3],[0,1,2,3]],"x":3,"candidate":[1]}。請依 [n,x,point_qualified,candidate,x_in_candidate,candidate_open,neighborhood] 欄序回答。

查看答案與解釋(4, 3, 是, [1], 否, 否, 否)

第二批擴展核對=(4, 3, 是, [1], 否, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0041/)

鄰域 · qf-ext19-neighborhood-qualification · candidate





## 42. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-qualification；資料={"n":4,"opens":[[],[0],[0,2],[0,2,3],[0,1,2,3]],"x":0,"candidate":[0,1]}。請依 [n,x,point_qualified,candidate,x_in_candidate,candidate_open,neighborhood] 欄序回答。

查看答案與解釋(4, 0, 是, [0, 1], 是, 否, 是)

第二批擴展核對=(4, 0, 是, [0, 1], 是, 否, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0042/)

鄰域 · qf-ext19-neighborhood-qualification · candidate





## 43. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-qualification；資料={"n":4,"opens":[[],[1],[1,2],[1,2,3],[0,1,2,3]],"x":1,"candidate":[2]}。請依 [n,x,point_qualified,candidate,x_in_candidate,candidate_open,neighborhood] 欄序回答。

查看答案與解釋(4, 1, 是, [2], 否, 否, 否)

第二批擴展核對=(4, 1, 是, [2], 否, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0043/)

鄰域 · qf-ext19-neighborhood-qualification · candidate





## 44. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-qualification；資料={"n":4,"opens":[[],[2],[1,2],[1,2,3],[0,1,2,3]],"x":2,"candidate":[0,2]}。請依 [n,x,point_qualified,candidate,x_in_candidate,candidate_open,neighborhood] 欄序回答。

查看答案與解釋(4, 2, 是, [0, 2], 是, 否, 是)

第二批擴展核對=(4, 2, 是, [0, 2], 是, 否, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0044/)

鄰域 · qf-ext19-neighborhood-qualification · candidate





## 45. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-qualification；資料={"n":4,"opens":[[],[3],[1,3],[1,2,3],[0,1,2,3]],"x":-1,"candidate":[1,2]}。請依 [n,x,point_qualified,candidate,x_in_candidate,candidate_open,neighborhood] 欄序回答。

查看答案與解釋(4, -1, 否, [1, 2], 不求值, 不求值, 不求值)

第二批擴展核對=(4, -1, 否, [1, 2], 不求值, 不求值, 不求值)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0045/)

鄰域 · qf-ext19-neighborhood-qualification · candidate





## 46. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-qualification；資料={"n":4,"opens":[[],[0],[0,3],[0,2,3],[0,1,2,3]],"x":0,"candidate":[0,1,2]}。請依 [n,x,point_qualified,candidate,x_in_candidate,candidate_open,neighborhood] 欄序回答。

查看答案與解釋(4, 0, 是, [0, 1, 2], 是, 否, 是)

第二批擴展核對=(4, 0, 是, [0, 1, 2], 是, 否, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0046/)

鄰域 · qf-ext19-neighborhood-qualification · candidate





## 47. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-qualification；資料={"n":4,"opens":[[],[1],[1,3],[1,2,3],[0,1,2,3]],"x":1,"candidate":[3]}。請依 [n,x,point_qualified,candidate,x_in_candidate,candidate_open,neighborhood] 欄序回答。

查看答案與解釋(4, 1, 是, [3], 否, 否, 否)

第二批擴展核對=(4, 1, 是, [3], 否, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0047/)

鄰域 · qf-ext19-neighborhood-qualification · candidate





## 48. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-qualification；資料={"n":4,"opens":[[],[2],[2,3],[1,2,3],[0,1,2,3]],"x":2,"candidate":[0,3]}。請依 [n,x,point_qualified,candidate,x_in_candidate,candidate_open,neighborhood] 欄序回答。

查看答案與解釋(4, 2, 是, [0, 3], 否, 否, 否)

第二批擴展核對=(4, 2, 是, [0, 3], 否, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0048/)

鄰域 · qf-ext19-neighborhood-qualification · candidate





## 49. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-qualification；資料={"n":4,"opens":[[],[3],[2,3],[1,2,3],[0,1,2,3]],"x":3,"candidate":[1,3]}。請依 [n,x,point_qualified,candidate,x_in_candidate,candidate_open,neighborhood] 欄序回答。

查看答案與解釋(4, 3, 是, [1, 3], 是, 否, 是)

第二批擴展核對=(4, 3, 是, [1, 3], 是, 否, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0049/)

鄰域 · qf-ext19-neighborhood-qualification · candidate





## 50. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-qualification；資料={"n":3,"opens":[[],[0],[0,1],[0,1,2]],"x":-1,"candidate":[0,1]}。請依 [n,x,point_qualified,candidate,x_in_candidate,candidate_open,neighborhood] 欄序回答。

查看答案與解釋(3, -1, 否, [0, 1], 不求值, 不求值, 不求值)

第二批擴展核對=(3, -1, 否, [0, 1], 不求值, 不求值, 不求值)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0050/)

鄰域 · qf-ext19-neighborhood-qualification · candidate





## 51. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-upward-closure；資料={"n":4,"opens":[[],[0],[0,1],[0,1,2],[0,1,2,3]],"x":0,"small":[0],"large":[0,1,2,3]}。請依 [n,x,point_qualified,small,large,small_subset_large,small_neighborhood,large_neighborhood] 欄序回答。

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

第二批擴展核對=(4, 0, 是, [0], [0, 1, 2, 3], 是, 是, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0051/)

鄰域 · qf-ext19-neighborhood-upward-closure · candidate





## 52. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-upward-closure；資料={"n":4,"opens":[[],[1],[0,1],[0,1,2],[0,1,2,3]],"x":1,"small":[1],"large":[0,1,2,3]}。請依 [n,x,point_qualified,small,large,small_subset_large,small_neighborhood,large_neighborhood] 欄序回答。

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

第二批擴展核對=(4, 1, 是, [1], [0, 1, 2, 3], 是, 是, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0052/)

鄰域 · qf-ext19-neighborhood-upward-closure · candidate





## 53. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-upward-closure；資料={"n":4,"opens":[[],[2],[0,2],[0,1,2],[0,1,2,3]],"x":2,"small":[2],"large":[0,1,2,3]}。請依 [n,x,point_qualified,small,large,small_subset_large,small_neighborhood,large_neighborhood] 欄序回答。

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

第二批擴展核對=(4, 2, 是, [2], [0, 1, 2, 3], 是, 是, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0053/)

鄰域 · qf-ext19-neighborhood-upward-closure · candidate





## 54. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-upward-closure；資料={"n":4,"opens":[[],[3],[0,3],[0,1,3],[0,1,2,3]],"x":3,"small":[3],"large":[0,1,2,3]}。請依 [n,x,point_qualified,small,large,small_subset_large,small_neighborhood,large_neighborhood] 欄序回答。

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

第二批擴展核對=(4, 3, 是, [3], [0, 1, 2, 3], 是, 是, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0054/)

鄰域 · qf-ext19-neighborhood-upward-closure · candidate





## 55. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-upward-closure；資料={"n":4,"opens":[[],[0],[0,2],[0,1,2],[0,1,2,3]],"x":-1,"small":[0],"large":[0,1,2,3]}。請依 [n,x,point_qualified,small,large,small_subset_large,small_neighborhood,large_neighborhood] 欄序回答。

查看答案與解釋(4, -1, 否, [0], [0, 1, 2, 3], 是, 不求值, 不求值)

第二批擴展核對=(4, -1, 否, [0], [0, 1, 2, 3], 是, 不求值, 不求值)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0055/)

鄰域 · qf-ext19-neighborhood-upward-closure · candidate





## 56. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-upward-closure；資料={"n":4,"opens":[[],[1],[1,2],[0,1,2],[0,1,2,3]],"x":1,"small":[1],"large":[0,1,2,3]}。請依 [n,x,point_qualified,small,large,small_subset_large,small_neighborhood,large_neighborhood] 欄序回答。

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

第二批擴展核對=(4, 1, 是, [1], [0, 1, 2, 3], 是, 是, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0056/)

鄰域 · qf-ext19-neighborhood-upward-closure · candidate





## 57. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-upward-closure；資料={"n":4,"opens":[[],[2],[1,2],[0,1,2],[0,1,2,3]],"x":2,"small":[2],"large":[0,1,2,3]}。請依 [n,x,point_qualified,small,large,small_subset_large,small_neighborhood,large_neighborhood] 欄序回答。

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

第二批擴展核對=(4, 2, 是, [2], [0, 1, 2, 3], 是, 是, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0057/)

鄰域 · qf-ext19-neighborhood-upward-closure · candidate





## 58. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-upward-closure；資料={"n":4,"opens":[[],[3],[1,3],[0,1,3],[0,1,2,3]],"x":3,"small":[3],"large":[0,1,2,3]}。請依 [n,x,point_qualified,small,large,small_subset_large,small_neighborhood,large_neighborhood] 欄序回答。

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

第二批擴展核對=(4, 3, 是, [3], [0, 1, 2, 3], 是, 是, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0058/)

鄰域 · qf-ext19-neighborhood-upward-closure · candidate





## 59. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-upward-closure；資料={"n":4,"opens":[[],[0],[0,3],[0,1,3],[0,1,2,3]],"x":0,"small":[0],"large":[0,1,2,3]}。請依 [n,x,point_qualified,small,large,small_subset_large,small_neighborhood,large_neighborhood] 欄序回答。

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

第二批擴展核對=(4, 0, 是, [0], [0, 1, 2, 3], 是, 是, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0059/)

鄰域 · qf-ext19-neighborhood-upward-closure · candidate





## 60. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-upward-closure；資料={"n":4,"opens":[[],[1],[1,3],[0,1,3],[0,1,2,3]],"x":-1,"small":[0,1,3],"large":[0,1,2,3]}。請依 [n,x,point_qualified,small,large,small_subset_large,small_neighborhood,large_neighborhood] 欄序回答。

查看答案與解釋(4, -1, 否, [0, 1, 3], [0, 1, 2, 3], 是, 不求值, 不求值)

第二批擴展核對=(4, -1, 否, [0, 1, 3], [0, 1, 2, 3], 是, 不求值, 不求值)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0060/)

鄰域 · qf-ext19-neighborhood-upward-closure · candidate





## 61. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-upward-closure；資料={"n":4,"opens":[[],[2],[2,3],[0,2,3],[0,1,2,3]],"x":2,"small":[2],"large":[0,1,2,3]}。請依 [n,x,point_qualified,small,large,small_subset_large,small_neighborhood,large_neighborhood] 欄序回答。

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

第二批擴展核對=(4, 2, 是, [2], [0, 1, 2, 3], 是, 是, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0061/)

鄰域 · qf-ext19-neighborhood-upward-closure · candidate





## 62. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-upward-closure；資料={"n":4,"opens":[[],[3],[2,3],[0,2,3],[0,1,2,3]],"x":3,"small":[3],"large":[0,1,2,3]}。請依 [n,x,point_qualified,small,large,small_subset_large,small_neighborhood,large_neighborhood] 欄序回答。

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

第二批擴展核對=(4, 3, 是, [3], [0, 1, 2, 3], 是, 是, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0062/)

鄰域 · qf-ext19-neighborhood-upward-closure · candidate





## 63. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-upward-closure；資料={"n":4,"opens":[[],[0],[0,1],[0,1,3],[0,1,2,3]],"x":0,"small":[0],"large":[0,1,2,3]}。請依 [n,x,point_qualified,small,large,small_subset_large,small_neighborhood,large_neighborhood] 欄序回答。

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

第二批擴展核對=(4, 0, 是, [0], [0, 1, 2, 3], 是, 是, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0063/)

鄰域 · qf-ext19-neighborhood-upward-closure · candidate





## 64. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-upward-closure；資料={"n":4,"opens":[[],[1],[0,1],[0,1,3],[0,1,2,3]],"x":1,"small":[1],"large":[0,1,2,3]}。請依 [n,x,point_qualified,small,large,small_subset_large,small_neighborhood,large_neighborhood] 欄序回答。

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

第二批擴展核對=(4, 1, 是, [1], [0, 1, 2, 3], 是, 是, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0064/)

鄰域 · qf-ext19-neighborhood-upward-closure · candidate





## 65. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-upward-closure；資料={"n":4,"opens":[[],[2],[0,2],[0,2,3],[0,1,2,3]],"x":-1,"small":[0,2],"large":[0,1,2,3]}。請依 [n,x,point_qualified,small,large,small_subset_large,small_neighborhood,large_neighborhood] 欄序回答。

查看答案與解釋(4, -1, 否, [0, 2], [0, 1, 2, 3], 是, 不求值, 不求值)

第二批擴展核對=(4, -1, 否, [0, 2], [0, 1, 2, 3], 是, 不求值, 不求值)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0065/)

鄰域 · qf-ext19-neighborhood-upward-closure · candidate





## 66. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-upward-closure；資料={"n":4,"opens":[[],[3],[0,3],[0,2,3],[0,1,2,3]],"x":3,"small":[3],"large":[0,1,2,3]}。請依 [n,x,point_qualified,small,large,small_subset_large,small_neighborhood,large_neighborhood] 欄序回答。

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

第二批擴展核對=(4, 3, 是, [3], [0, 1, 2, 3], 是, 是, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0066/)

鄰域 · qf-ext19-neighborhood-upward-closure · candidate





## 67. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-upward-closure；資料={"n":4,"opens":[[],[0],[0,2],[0,2,3],[0,1,2,3]],"x":0,"small":[0],"large":[0,1,2,3]}。請依 [n,x,point_qualified,small,large,small_subset_large,small_neighborhood,large_neighborhood] 欄序回答。

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

第二批擴展核對=(4, 0, 是, [0], [0, 1, 2, 3], 是, 是, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0067/)

鄰域 · qf-ext19-neighborhood-upward-closure · candidate





## 68. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-upward-closure；資料={"n":4,"opens":[[],[1],[1,2],[1,2,3],[0,1,2,3]],"x":1,"small":[1],"large":[0,1,2,3]}。請依 [n,x,point_qualified,small,large,small_subset_large,small_neighborhood,large_neighborhood] 欄序回答。

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

第二批擴展核對=(4, 1, 是, [1], [0, 1, 2, 3], 是, 是, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0068/)

鄰域 · qf-ext19-neighborhood-upward-closure · candidate





## 69. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-upward-closure；資料={"n":4,"opens":[[],[2],[1,2],[1,2,3],[0,1,2,3]],"x":2,"small":[2],"large":[0,1,2,3]}。請依 [n,x,point_qualified,small,large,small_subset_large,small_neighborhood,large_neighborhood] 欄序回答。

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

第二批擴展核對=(4, 2, 是, [2], [0, 1, 2, 3], 是, 是, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0069/)

鄰域 · qf-ext19-neighborhood-upward-closure · candidate





## 70. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-upward-closure；資料={"n":4,"opens":[[],[3],[1,3],[1,2,3],[0,1,2,3]],"x":-1,"small":[0,1,2,3],"large":[0,1,2,3]}。請依 [n,x,point_qualified,small,large,small_subset_large,small_neighborhood,large_neighborhood] 欄序回答。

查看答案與解釋(4, -1, 否, [0, 1, 2, 3], [0, 1, 2, 3], 是, 不求值, 不求值)

第二批擴展核對=(4, -1, 否, [0, 1, 2, 3], [0, 1, 2, 3], 是, 不求值, 不求值)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0070/)

鄰域 · qf-ext19-neighborhood-upward-closure · candidate





## 71. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-upward-closure；資料={"n":4,"opens":[[],[0],[0,3],[0,2,3],[0,1,2,3]],"x":0,"small":[0],"large":[0,1,2,3]}。請依 [n,x,point_qualified,small,large,small_subset_large,small_neighborhood,large_neighborhood] 欄序回答。

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

第二批擴展核對=(4, 0, 是, [0], [0, 1, 2, 3], 是, 是, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0071/)

鄰域 · qf-ext19-neighborhood-upward-closure · candidate





## 72. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-upward-closure；資料={"n":4,"opens":[[],[1],[1,3],[1,2,3],[0,1,2,3]],"x":1,"small":[1],"large":[0,1,2,3]}。請依 [n,x,point_qualified,small,large,small_subset_large,small_neighborhood,large_neighborhood] 欄序回答。

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

第二批擴展核對=(4, 1, 是, [1], [0, 1, 2, 3], 是, 是, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0072/)

鄰域 · qf-ext19-neighborhood-upward-closure · candidate





## 73. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-upward-closure；資料={"n":4,"opens":[[],[2],[2,3],[1,2,3],[0,1,2,3]],"x":2,"small":[2],"large":[0,1,2,3]}。請依 [n,x,point_qualified,small,large,small_subset_large,small_neighborhood,large_neighborhood] 欄序回答。

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

第二批擴展核對=(4, 2, 是, [2], [0, 1, 2, 3], 是, 是, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0073/)

鄰域 · qf-ext19-neighborhood-upward-closure · candidate





## 74. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-upward-closure；資料={"n":4,"opens":[[],[3],[2,3],[1,2,3],[0,1,2,3]],"x":3,"small":[3],"large":[0,1,2,3]}。請依 [n,x,point_qualified,small,large,small_subset_large,small_neighborhood,large_neighborhood] 欄序回答。

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

第二批擴展核對=(4, 3, 是, [3], [0, 1, 2, 3], 是, 是, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0074/)

鄰域 · qf-ext19-neighborhood-upward-closure · candidate





## 75. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-upward-closure；資料={"n":3,"opens":[[],[0],[0,1],[0,1,2]],"x":-1,"small":[0],"large":[0,1,2]}。請依 [n,x,point_qualified,small,large,small_subset_large,small_neighborhood,large_neighborhood] 欄序回答。

查看答案與解釋(3, -1, 否, [0], [0, 1, 2], 是, 不求值, 不求值)

第二批擴展核對=(3, -1, 否, [0], [0, 1, 2], 是, 不求值, 不求值)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0075/)

鄰域 · qf-ext19-neighborhood-upward-closure · candidate





## 76. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-complete-inventory；資料={"n":4,"opens":[[],[0],[0,1],[0,1,2],[0,1,2,3]],"x":0}。請依 [n,x,open_basis,all_neighborhoods] 欄序回答。

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

第二批擴展核對=(4, 0, [[0], [0, 1], [0, 1, 2], [0, 1, 2, 3]], [[0], [0, 1], [0, 2], [0, 1, 2], [0, 3], [0, 1, 3], [0, 2, 3], [0, 1, 2, 3]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0076/)

鄰域 · qf-ext19-neighborhood-complete-inventory · candidate





## 77. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-complete-inventory；資料={"n":4,"opens":[[],[1],[0,1],[0,1,2],[0,1,2,3]],"x":1}。請依 [n,x,open_basis,all_neighborhoods] 欄序回答。

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

第二批擴展核對=(4, 1, [[1], [0, 1], [0, 1, 2], [0, 1, 2, 3]], [[1], [0, 1], [1, 2], [0, 1, 2], [1, 3], [0, 1, 3], [1, 2, 3], [0, 1, 2, 3]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0077/)

鄰域 · qf-ext19-neighborhood-complete-inventory · candidate





## 78. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-complete-inventory；資料={"n":4,"opens":[[],[2],[0,2],[0,1,2],[0,1,2,3]],"x":2}。請依 [n,x,open_basis,all_neighborhoods] 欄序回答。

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

第二批擴展核對=(4, 2, [[2], [0, 2], [0, 1, 2], [0, 1, 2, 3]], [[2], [0, 2], [1, 2], [0, 1, 2], [2, 3], [0, 2, 3], [1, 2, 3], [0, 1, 2, 3]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0078/)

鄰域 · qf-ext19-neighborhood-complete-inventory · candidate





## 79. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-complete-inventory；資料={"n":4,"opens":[[],[3],[0,3],[0,1,3],[0,1,2,3]],"x":3}。請依 [n,x,open_basis,all_neighborhoods] 欄序回答。

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

第二批擴展核對=(4, 3, [[3], [0, 3], [0, 1, 3], [0, 1, 2, 3]], [[3], [0, 3], [1, 3], [0, 1, 3], [2, 3], [0, 2, 3], [1, 2, 3], [0, 1, 2, 3]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0079/)

鄰域 · qf-ext19-neighborhood-complete-inventory · candidate





## 80. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-complete-inventory；資料={"n":4,"opens":[[],[0],[0,2],[0,1,2],[0,1,2,3]],"x":0}。請依 [n,x,open_basis,all_neighborhoods] 欄序回答。

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

第二批擴展核對=(4, 0, [[0], [0, 2], [0, 1, 2], [0, 1, 2, 3]], [[0], [0, 1], [0, 2], [0, 1, 2], [0, 3], [0, 1, 3], [0, 2, 3], [0, 1, 2, 3]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0080/)

鄰域 · qf-ext19-neighborhood-complete-inventory · candidate





## 81. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-complete-inventory；資料={"n":4,"opens":[[],[1],[1,2],[0,1,2],[0,1,2,3]],"x":1}。請依 [n,x,open_basis,all_neighborhoods] 欄序回答。

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

第二批擴展核對=(4, 1, [[1], [1, 2], [0, 1, 2], [0, 1, 2, 3]], [[1], [0, 1], [1, 2], [0, 1, 2], [1, 3], [0, 1, 3], [1, 2, 3], [0, 1, 2, 3]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0081/)

鄰域 · qf-ext19-neighborhood-complete-inventory · candidate





## 82. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-complete-inventory；資料={"n":4,"opens":[[],[2],[1,2],[0,1,2],[0,1,2,3]],"x":2}。請依 [n,x,open_basis,all_neighborhoods] 欄序回答。

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

第二批擴展核對=(4, 2, [[2], [1, 2], [0, 1, 2], [0, 1, 2, 3]], [[2], [0, 2], [1, 2], [0, 1, 2], [2, 3], [0, 2, 3], [1, 2, 3], [0, 1, 2, 3]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0082/)

鄰域 · qf-ext19-neighborhood-complete-inventory · candidate





## 83. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-complete-inventory；資料={"n":4,"opens":[[],[3],[1,3],[0,1,3],[0,1,2,3]],"x":3}。請依 [n,x,open_basis,all_neighborhoods] 欄序回答。

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

第二批擴展核對=(4, 3, [[3], [1, 3], [0, 1, 3], [0, 1, 2, 3]], [[3], [0, 3], [1, 3], [0, 1, 3], [2, 3], [0, 2, 3], [1, 2, 3], [0, 1, 2, 3]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0083/)

鄰域 · qf-ext19-neighborhood-complete-inventory · candidate





## 84. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-complete-inventory；資料={"n":4,"opens":[[],[0],[0,3],[0,1,3],[0,1,2,3]],"x":0}。請依 [n,x,open_basis,all_neighborhoods] 欄序回答。

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

第二批擴展核對=(4, 0, [[0], [0, 3], [0, 1, 3], [0, 1, 2, 3]], [[0], [0, 1], [0, 2], [0, 1, 2], [0, 3], [0, 1, 3], [0, 2, 3], [0, 1, 2, 3]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0084/)

鄰域 · qf-ext19-neighborhood-complete-inventory · candidate





## 85. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-complete-inventory；資料={"n":4,"opens":[[],[1],[1,3],[0,1,3],[0,1,2,3]],"x":0}。請依 [n,x,open_basis,all_neighborhoods] 欄序回答。

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

第二批擴展核對=(4, 0, [[0, 1, 3], [0, 1, 2, 3]], [[0, 1, 3], [0, 1, 2, 3]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0085/)

鄰域 · qf-ext19-neighborhood-complete-inventory · candidate





## 86. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-complete-inventory；資料={"n":4,"opens":[[],[2],[2,3],[0,2,3],[0,1,2,3]],"x":2}。請依 [n,x,open_basis,all_neighborhoods] 欄序回答。

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

第二批擴展核對=(4, 2, [[2], [2, 3], [0, 2, 3], [0, 1, 2, 3]], [[2], [0, 2], [1, 2], [0, 1, 2], [2, 3], [0, 2, 3], [1, 2, 3], [0, 1, 2, 3]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0086/)

鄰域 · qf-ext19-neighborhood-complete-inventory · candidate





## 87. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-complete-inventory；資料={"n":4,"opens":[[],[3],[2,3],[0,2,3],[0,1,2,3]],"x":3}。請依 [n,x,open_basis,all_neighborhoods] 欄序回答。

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

第二批擴展核對=(4, 3, [[3], [2, 3], [0, 2, 3], [0, 1, 2, 3]], [[3], [0, 3], [1, 3], [0, 1, 3], [2, 3], [0, 2, 3], [1, 2, 3], [0, 1, 2, 3]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0087/)

鄰域 · qf-ext19-neighborhood-complete-inventory · candidate





## 88. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-complete-inventory；資料={"n":4,"opens":[[],[0],[0,1],[0,1,3],[0,1,2,3]],"x":0}。請依 [n,x,open_basis,all_neighborhoods] 欄序回答。

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

第二批擴展核對=(4, 0, [[0], [0, 1], [0, 1, 3], [0, 1, 2, 3]], [[0], [0, 1], [0, 2], [0, 1, 2], [0, 3], [0, 1, 3], [0, 2, 3], [0, 1, 2, 3]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0088/)

鄰域 · qf-ext19-neighborhood-complete-inventory · candidate





## 89. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-complete-inventory；資料={"n":4,"opens":[[],[1],[0,1],[0,1,3],[0,1,2,3]],"x":1}。請依 [n,x,open_basis,all_neighborhoods] 欄序回答。

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

第二批擴展核對=(4, 1, [[1], [0, 1], [0, 1, 3], [0, 1, 2, 3]], [[1], [0, 1], [1, 2], [0, 1, 2], [1, 3], [0, 1, 3], [1, 2, 3], [0, 1, 2, 3]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0089/)

鄰域 · qf-ext19-neighborhood-complete-inventory · candidate





## 90. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-complete-inventory；資料={"n":4,"opens":[[],[2],[0,2],[0,2,3],[0,1,2,3]],"x":0}。請依 [n,x,open_basis,all_neighborhoods] 欄序回答。

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

第二批擴展核對=(4, 0, [[0, 2], [0, 2, 3], [0, 1, 2, 3]], [[0, 2], [0, 1, 2], [0, 2, 3], [0, 1, 2, 3]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0090/)

鄰域 · qf-ext19-neighborhood-complete-inventory · candidate





## 91. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-complete-inventory；資料={"n":4,"opens":[[],[3],[0,3],[0,2,3],[0,1,2,3]],"x":3}。請依 [n,x,open_basis,all_neighborhoods] 欄序回答。

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

第二批擴展核對=(4, 3, [[3], [0, 3], [0, 2, 3], [0, 1, 2, 3]], [[3], [0, 3], [1, 3], [0, 1, 3], [2, 3], [0, 2, 3], [1, 2, 3], [0, 1, 2, 3]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0091/)

鄰域 · qf-ext19-neighborhood-complete-inventory · candidate





## 92. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-complete-inventory；資料={"n":4,"opens":[[],[0],[0,2],[0,2,3],[0,1,2,3]],"x":0}。請依 [n,x,open_basis,all_neighborhoods] 欄序回答。

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

第二批擴展核對=(4, 0, [[0], [0, 2], [0, 2, 3], [0, 1, 2, 3]], [[0], [0, 1], [0, 2], [0, 1, 2], [0, 3], [0, 1, 3], [0, 2, 3], [0, 1, 2, 3]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0092/)

鄰域 · qf-ext19-neighborhood-complete-inventory · candidate





## 93. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-complete-inventory；資料={"n":4,"opens":[[],[1],[1,2],[1,2,3],[0,1,2,3]],"x":1}。請依 [n,x,open_basis,all_neighborhoods] 欄序回答。

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

第二批擴展核對=(4, 1, [[1], [1, 2], [1, 2, 3], [0, 1, 2, 3]], [[1], [0, 1], [1, 2], [0, 1, 2], [1, 3], [0, 1, 3], [1, 2, 3], [0, 1, 2, 3]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0093/)

鄰域 · qf-ext19-neighborhood-complete-inventory · candidate





## 94. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-complete-inventory；資料={"n":4,"opens":[[],[2],[1,2],[1,2,3],[0,1,2,3]],"x":2}。請依 [n,x,open_basis,all_neighborhoods] 欄序回答。

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

第二批擴展核對=(4, 2, [[2], [1, 2], [1, 2, 3], [0, 1, 2, 3]], [[2], [0, 2], [1, 2], [0, 1, 2], [2, 3], [0, 2, 3], [1, 2, 3], [0, 1, 2, 3]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0094/)

鄰域 · qf-ext19-neighborhood-complete-inventory · candidate





## 95. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-complete-inventory；資料={"n":4,"opens":[[],[3],[1,3],[1,2,3],[0,1,2,3]],"x":0}。請依 [n,x,open_basis,all_neighborhoods] 欄序回答。

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

第二批擴展核對=(4, 0, [[0, 1, 2, 3]], [[0, 1, 2, 3]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0095/)

鄰域 · qf-ext19-neighborhood-complete-inventory · candidate





## 96. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-complete-inventory；資料={"n":4,"opens":[[],[0],[0,3],[0,2,3],[0,1,2,3]],"x":0}。請依 [n,x,open_basis,all_neighborhoods] 欄序回答。

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

第二批擴展核對=(4, 0, [[0], [0, 3], [0, 2, 3], [0, 1, 2, 3]], [[0], [0, 1], [0, 2], [0, 1, 2], [0, 3], [0, 1, 3], [0, 2, 3], [0, 1, 2, 3]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0096/)

鄰域 · qf-ext19-neighborhood-complete-inventory · candidate





## 97. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-complete-inventory；資料={"n":4,"opens":[[],[1],[1,3],[1,2,3],[0,1,2,3]],"x":1}。請依 [n,x,open_basis,all_neighborhoods] 欄序回答。

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

第二批擴展核對=(4, 1, [[1], [1, 3], [1, 2, 3], [0, 1, 2, 3]], [[1], [0, 1], [1, 2], [0, 1, 2], [1, 3], [0, 1, 3], [1, 2, 3], [0, 1, 2, 3]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0097/)

鄰域 · qf-ext19-neighborhood-complete-inventory · candidate





## 98. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-complete-inventory；資料={"n":4,"opens":[[],[2],[2,3],[1,2,3],[0,1,2,3]],"x":2}。請依 [n,x,open_basis,all_neighborhoods] 欄序回答。

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

第二批擴展核對=(4, 2, [[2], [2, 3], [1, 2, 3], [0, 1, 2, 3]], [[2], [0, 2], [1, 2], [0, 1, 2], [2, 3], [0, 2, 3], [1, 2, 3], [0, 1, 2, 3]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0098/)

鄰域 · qf-ext19-neighborhood-complete-inventory · candidate





## 99. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-complete-inventory；資料={"n":4,"opens":[[],[3],[2,3],[1,2,3],[0,1,2,3]],"x":3}。請依 [n,x,open_basis,all_neighborhoods] 欄序回答。

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

第二批擴展核對=(4, 3, [[3], [2, 3], [1, 2, 3], [0, 1, 2, 3]], [[3], [0, 3], [1, 3], [0, 1, 3], [2, 3], [0, 2, 3], [1, 2, 3], [0, 1, 2, 3]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0099/)

鄰域 · qf-ext19-neighborhood-complete-inventory · candidate





## 100. 鄰域與開集見證

完整有限拓撲與指定點。操作=neighborhood-complete-inventory；資料={"n":3,"opens":[[],[0],[0,1],[0,1,2]],"x":0}。請依 [n,x,open_basis,all_neighborhoods] 欄序回答。

查看答案與解釋(3, 0, [[0], [0, 1], [0, 1, 2]], [[0], [0, 1], [0, 2], [0, 1, 2]])

第二批擴展核對=(3, 0, [[0], [0, 1], [0, 1, 2]], [[0], [0, 1], [0, 2], [0, 1, 2]])；依完整明示資料重算；有限／合成資料核對不是一般形式證明；鄰域包含含點開集；鄰域本身不必開；域外點不求值。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261019-r02-neighborhood-0100/)

鄰域 · qf-ext19-neighborhood-complete-inventory · candidate



[原始題目 JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261013-advance-20261019-r02-neighborhood-foundations/questions.jsonl) · [驗收報告](https://ocme.evemisslab.com/data/questions/batches/batch-20261013-advance-20261019-r02-neighborhood-foundations/validation-report.json)