# Hausdorff空間基礎 · 脈衝 R03

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

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

batch-20261014-advance-20261111-r03-hausdorff-space-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. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-pair-separator；資料={"points":["a0","b0","c0"],"topology":[["a0","b0","c0"],["a0","b0"],["a0","c0"],["a0"],["b0","c0"],["b0"],["c0"],[]],"x":"a0","y":"b0"}。請依 [x, y, open_neighborhood_witness, separated, witness_disjoint] 欄序回答。

查看答案與解釋(a0, b0, [[a0, c0], [b0]], 是, 是)

Wave6第五層核對=(a0, b0, [[a0, c0], [b0]], 是, 是)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0001/)

Hausdorff空間 · qf-mod42-hausdorff-pair-separator · candidate





## 2. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-pair-separator；資料={"points":["a1","b1","c1"],"topology":[["a1","b1","c1"],["a1","b1"],["a1","c1"],["a1"],["b1","c1"],["b1"],["c1"],[]],"x":"a1","y":"b1"}。請依 [x, y, open_neighborhood_witness, separated, witness_disjoint] 欄序回答。

查看答案與解釋(a1, b1, [[a1, c1], [b1]], 是, 是)

Wave6第五層核對=(a1, b1, [[a1, c1], [b1]], 是, 是)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0002/)

Hausdorff空間 · qf-mod42-hausdorff-pair-separator · candidate





## 3. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-pair-separator；資料={"points":["a2","b2","c2"],"topology":[["a2","b2","c2"],["a2","b2"],["a2","c2"],["a2"],["b2","c2"],["b2"],["c2"],[]],"x":"a2","y":"b2"}。請依 [x, y, open_neighborhood_witness, separated, witness_disjoint] 欄序回答。

查看答案與解釋(a2, b2, [[a2, c2], [b2]], 是, 是)

Wave6第五層核對=(a2, b2, [[a2, c2], [b2]], 是, 是)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0003/)

Hausdorff空間 · qf-mod42-hausdorff-pair-separator · candidate





## 4. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-pair-separator；資料={"points":["a3","b3","c3"],"topology":[["a3","b3","c3"],["a3","b3"],["a3","c3"],["a3"],["b3","c3"],["b3"],["c3"],[]],"x":"a3","y":"b3"}。請依 [x, y, open_neighborhood_witness, separated, witness_disjoint] 欄序回答。

查看答案與解釋(a3, b3, [[a3, c3], [b3]], 是, 是)

Wave6第五層核對=(a3, b3, [[a3, c3], [b3]], 是, 是)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0004/)

Hausdorff空間 · qf-mod42-hausdorff-pair-separator · candidate





## 5. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-pair-separator；資料={"points":["a4","b4","c4"],"topology":[["a4","b4","c4"],["a4","b4"],["a4","c4"],["a4"],["b4","c4"],["b4"],["c4"],[]],"x":"a4","y":"b4"}。請依 [x, y, open_neighborhood_witness, separated, witness_disjoint] 欄序回答。

查看答案與解釋(a4, b4, [[a4, c4], [b4]], 是, 是)

Wave6第五層核對=(a4, b4, [[a4, c4], [b4]], 是, 是)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0005/)

Hausdorff空間 · qf-mod42-hausdorff-pair-separator · candidate





## 6. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-pair-separator；資料={"points":["a5","b5","c5"],"topology":[["a5","b5","c5"],["a5","b5"],["a5","c5"],["a5"],["b5","c5"],["b5"],["c5"],[]],"x":"a5","y":"b5"}。請依 [x, y, open_neighborhood_witness, separated, witness_disjoint] 欄序回答。

查看答案與解釋(a5, b5, [[a5, c5], [b5]], 是, 是)

Wave6第五層核對=(a5, b5, [[a5, c5], [b5]], 是, 是)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0006/)

Hausdorff空間 · qf-mod42-hausdorff-pair-separator · candidate





## 7. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-pair-separator；資料={"points":["a6","b6","c6"],"topology":[["a6","b6","c6"],["a6","b6"],["a6","c6"],["a6"],["b6","c6"],["b6"],["c6"],[]],"x":"a6","y":"b6"}。請依 [x, y, open_neighborhood_witness, separated, witness_disjoint] 欄序回答。

查看答案與解釋(a6, b6, [[a6, c6], [b6]], 是, 是)

Wave6第五層核對=(a6, b6, [[a6, c6], [b6]], 是, 是)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0007/)

Hausdorff空間 · qf-mod42-hausdorff-pair-separator · candidate





## 8. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-pair-separator；資料={"points":["a7","b7","c7"],"topology":[["a7","b7","c7"],["a7","b7"],["a7","c7"],["a7"],["b7","c7"],["b7"],["c7"],[]],"x":"a7","y":"b7"}。請依 [x, y, open_neighborhood_witness, separated, witness_disjoint] 欄序回答。

查看答案與解釋(a7, b7, [[a7, c7], [b7]], 是, 是)

Wave6第五層核對=(a7, b7, [[a7, c7], [b7]], 是, 是)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0008/)

Hausdorff空間 · qf-mod42-hausdorff-pair-separator · candidate





## 9. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-pair-separator；資料={"points":["a8","b8","c8"],"topology":[["a8","b8","c8"],["a8","b8"],["a8","c8"],["a8"],["b8","c8"],["b8"],["c8"],[]],"x":"a8","y":"b8"}。請依 [x, y, open_neighborhood_witness, separated, witness_disjoint] 欄序回答。

查看答案與解釋(a8, b8, [[a8, c8], [b8]], 是, 是)

Wave6第五層核對=(a8, b8, [[a8, c8], [b8]], 是, 是)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0009/)

Hausdorff空間 · qf-mod42-hausdorff-pair-separator · candidate





## 10. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-pair-separator；資料={"points":["a9","b9","c9"],"topology":[["a9","b9","c9"],["a9","b9"],["a9","c9"],["a9"],["b9","c9"],["b9"],["c9"],[]],"x":"a9","y":"b9"}。請依 [x, y, open_neighborhood_witness, separated, witness_disjoint] 欄序回答。

查看答案與解釋(a9, b9, [[a9, c9], [b9]], 是, 是)

Wave6第五層核對=(a9, b9, [[a9, c9], [b9]], 是, 是)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0010/)

Hausdorff空間 · qf-mod42-hausdorff-pair-separator · candidate





## 11. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-pair-separator；資料={"points":["a10","b10","c10"],"topology":[["a10","b10","c10"],["a10","b10"],["a10","c10"],["a10"],["b10","c10"],["b10"],["c10"],[]],"x":"a10","y":"b10"}。請依 [x, y, open_neighborhood_witness, separated, witness_disjoint] 欄序回答。

查看答案與解釋(a10, b10, [[a10, c10], [b10]], 是, 是)

Wave6第五層核對=(a10, b10, [[a10, c10], [b10]], 是, 是)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0011/)

Hausdorff空間 · qf-mod42-hausdorff-pair-separator · candidate





## 12. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-pair-separator；資料={"points":["a11","b11","c11"],"topology":[["a11","b11","c11"],["a11","b11"],["a11","c11"],["a11"],["b11","c11"],["b11"],["c11"],[]],"x":"a11","y":"b11"}。請依 [x, y, open_neighborhood_witness, separated, witness_disjoint] 欄序回答。

查看答案與解釋(a11, b11, [[a11, c11], [b11]], 是, 是)

Wave6第五層核對=(a11, b11, [[a11, c11], [b11]], 是, 是)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0012/)

Hausdorff空間 · qf-mod42-hausdorff-pair-separator · candidate





## 13. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-pair-separator；資料={"points":["a12","b12","c12"],"topology":[["a12","b12","c12"],["a12","b12"],["a12","c12"],["a12"],["b12","c12"],["b12"],["c12"],[]],"x":"a12","y":"b12"}。請依 [x, y, open_neighborhood_witness, separated, witness_disjoint] 欄序回答。

查看答案與解釋(a12, b12, [[a12, c12], [b12]], 是, 是)

Wave6第五層核對=(a12, b12, [[a12, c12], [b12]], 是, 是)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0013/)

Hausdorff空間 · qf-mod42-hausdorff-pair-separator · candidate





## 14. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-pair-separator；資料={"points":["a13","b13","c13"],"topology":[["a13","b13","c13"],["a13","b13"],["a13","c13"],["a13"],["b13","c13"],["b13"],["c13"],[]],"x":"a13","y":"b13"}。請依 [x, y, open_neighborhood_witness, separated, witness_disjoint] 欄序回答。

查看答案與解釋(a13, b13, [[a13, c13], [b13]], 是, 是)

Wave6第五層核對=(a13, b13, [[a13, c13], [b13]], 是, 是)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0014/)

Hausdorff空間 · qf-mod42-hausdorff-pair-separator · candidate





## 15. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-pair-separator；資料={"points":["a14","b14","c14"],"topology":[["a14","b14","c14"],["a14","b14"],["a14","c14"],["a14"],["b14","c14"],["b14"],["c14"],[]],"x":"a14","y":"b14"}。請依 [x, y, open_neighborhood_witness, separated, witness_disjoint] 欄序回答。

查看答案與解釋(a14, b14, [[a14, c14], [b14]], 是, 是)

Wave6第五層核對=(a14, b14, [[a14, c14], [b14]], 是, 是)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0015/)

Hausdorff空間 · qf-mod42-hausdorff-pair-separator · candidate





## 16. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-pair-separator；資料={"points":["a15","b15","c15"],"topology":[["a15","b15","c15"],["a15","b15"],["a15","c15"],["a15"],["b15","c15"],["b15"],["c15"],[]],"x":"a15","y":"b15"}。請依 [x, y, open_neighborhood_witness, separated, witness_disjoint] 欄序回答。

查看答案與解釋(a15, b15, [[a15, c15], [b15]], 是, 是)

Wave6第五層核對=(a15, b15, [[a15, c15], [b15]], 是, 是)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0016/)

Hausdorff空間 · qf-mod42-hausdorff-pair-separator · candidate





## 17. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-pair-separator；資料={"points":["a16","b16","c16"],"topology":[["a16","b16","c16"],["a16","b16"],["a16","c16"],["a16"],["b16","c16"],["b16"],["c16"],[]],"x":"a16","y":"b16"}。請依 [x, y, open_neighborhood_witness, separated, witness_disjoint] 欄序回答。

查看答案與解釋(a16, b16, [[a16, c16], [b16]], 是, 是)

Wave6第五層核對=(a16, b16, [[a16, c16], [b16]], 是, 是)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0017/)

Hausdorff空間 · qf-mod42-hausdorff-pair-separator · candidate





## 18. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-pair-separator；資料={"points":["a17","b17","c17"],"topology":[["a17","b17","c17"],["a17","b17"],["a17","c17"],["a17"],["b17","c17"],["b17"],["c17"],[]],"x":"a17","y":"b17"}。請依 [x, y, open_neighborhood_witness, separated, witness_disjoint] 欄序回答。

查看答案與解釋(a17, b17, [[a17, c17], [b17]], 是, 是)

Wave6第五層核對=(a17, b17, [[a17, c17], [b17]], 是, 是)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0018/)

Hausdorff空間 · qf-mod42-hausdorff-pair-separator · candidate





## 19. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-pair-separator；資料={"points":["a18","b18","c18"],"topology":[["a18","b18","c18"],["a18","b18"],["a18","c18"],["a18"],["b18","c18"],["b18"],["c18"],[]],"x":"a18","y":"b18"}。請依 [x, y, open_neighborhood_witness, separated, witness_disjoint] 欄序回答。

查看答案與解釋(a18, b18, [[a18, c18], [b18]], 是, 是)

Wave6第五層核對=(a18, b18, [[a18, c18], [b18]], 是, 是)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0019/)

Hausdorff空間 · qf-mod42-hausdorff-pair-separator · candidate





## 20. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-pair-separator；資料={"points":["a19","b19","c19"],"topology":[["a19","b19","c19"],["a19","b19"],["a19","c19"],["a19"],["b19","c19"],["b19"],["c19"],[]],"x":"a19","y":"b19"}。請依 [x, y, open_neighborhood_witness, separated, witness_disjoint] 欄序回答。

查看答案與解釋(a19, b19, [[a19, c19], [b19]], 是, 是)

Wave6第五層核對=(a19, b19, [[a19, c19], [b19]], 是, 是)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0020/)

Hausdorff空間 · qf-mod42-hausdorff-pair-separator · candidate





## 21. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-pair-separator；資料={"points":["a20","b20","c20"],"topology":[["a20","b20","c20"],["a20","b20"],["a20","c20"],["a20"],["b20","c20"],["b20"],["c20"],[]],"x":"a20","y":"b20"}。請依 [x, y, open_neighborhood_witness, separated, witness_disjoint] 欄序回答。

查看答案與解釋(a20, b20, [[a20, c20], [b20]], 是, 是)

Wave6第五層核對=(a20, b20, [[a20, c20], [b20]], 是, 是)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0021/)

Hausdorff空間 · qf-mod42-hausdorff-pair-separator · candidate





## 22. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-pair-separator；資料={"points":["a21","b21","c21"],"topology":[["a21","b21","c21"],["a21","b21"],["a21","c21"],["a21"],["b21","c21"],["b21"],["c21"],[]],"x":"a21","y":"b21"}。請依 [x, y, open_neighborhood_witness, separated, witness_disjoint] 欄序回答。

查看答案與解釋(a21, b21, [[a21, c21], [b21]], 是, 是)

Wave6第五層核對=(a21, b21, [[a21, c21], [b21]], 是, 是)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0022/)

Hausdorff空間 · qf-mod42-hausdorff-pair-separator · candidate





## 23. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-pair-separator；資料={"points":["a22","b22","c22"],"topology":[["a22","b22","c22"],["a22","b22"],["a22","c22"],["a22"],["b22","c22"],["b22"],["c22"],[]],"x":"a22","y":"b22"}。請依 [x, y, open_neighborhood_witness, separated, witness_disjoint] 欄序回答。

查看答案與解釋(a22, b22, [[a22, c22], [b22]], 是, 是)

Wave6第五層核對=(a22, b22, [[a22, c22], [b22]], 是, 是)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0023/)

Hausdorff空間 · qf-mod42-hausdorff-pair-separator · candidate





## 24. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-pair-separator；資料={"points":["a23","b23","c23"],"topology":[["a23","b23","c23"],["a23","b23"],["a23","c23"],["a23"],["b23","c23"],["b23"],["c23"],[]],"x":"a23","y":"b23"}。請依 [x, y, open_neighborhood_witness, separated, witness_disjoint] 欄序回答。

查看答案與解釋(a23, b23, [[a23, c23], [b23]], 是, 是)

Wave6第五層核對=(a23, b23, [[a23, c23], [b23]], 是, 是)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0024/)

Hausdorff空間 · qf-mod42-hausdorff-pair-separator · candidate





## 25. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-pair-separator；資料={"points":["a24","b24","c24"],"topology":[["a24","b24","c24"],["a24","b24"],["a24","c24"],["a24"],["b24","c24"],["b24"],["c24"],[]],"x":"a24","y":"b24"}。請依 [x, y, open_neighborhood_witness, separated, witness_disjoint] 欄序回答。

查看答案與解釋(a24, b24, [[a24, c24], [b24]], 是, 是)

Wave6第五層核對=(a24, b24, [[a24, c24], [b24]], 是, 是)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0025/)

Hausdorff空間 · qf-mod42-hausdorff-pair-separator · candidate





## 26. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-full-audit；資料={"points":["a0","b0","c0"],"topology":[["a0","b0","c0"],["a0","b0"],["a0","c0"],["a0"],["b0","c0"],["b0"],["c0"],[]]}。請依 [points, pair_witness_rows, Hausdorff, certificate] 欄序回答。

查看答案與解釋([a0, b0, c0], [[a0, b0, [[a0, c0], [b0]]], [a0, c0, [[a0, b0], [c0]]], [b0, c0, [[a0, b0], [c0]]]], 是, all_distinct_pairs_exhaustively_separated)

Wave6第五層核對=([a0, b0, c0], [[a0, b0, [[a0, c0], [b0]]], [a0, c0, [[a0, b0], [c0]]], [b0, c0, [[a0, b0], [c0]]]], 是, all_distinct_pairs_exhaustively_separated)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0026/)

Hausdorff空間 · qf-mod42-hausdorff-full-audit · candidate





## 27. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-full-audit；資料={"points":["a1","b1","c1"],"topology":[["a1","b1","c1"],["a1","b1"],["a1","c1"],["a1"],["b1","c1"],["b1"],["c1"],[]]}。請依 [points, pair_witness_rows, Hausdorff, certificate] 欄序回答。

查看答案與解釋([a1, b1, c1], [[a1, b1, [[a1, c1], [b1]]], [a1, c1, [[a1, b1], [c1]]], [b1, c1, [[a1, b1], [c1]]]], 是, all_distinct_pairs_exhaustively_separated)

Wave6第五層核對=([a1, b1, c1], [[a1, b1, [[a1, c1], [b1]]], [a1, c1, [[a1, b1], [c1]]], [b1, c1, [[a1, b1], [c1]]]], 是, all_distinct_pairs_exhaustively_separated)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0027/)

Hausdorff空間 · qf-mod42-hausdorff-full-audit · candidate





## 28. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-full-audit；資料={"points":["a2","b2","c2"],"topology":[["a2","b2","c2"],["a2","b2"],["a2","c2"],["a2"],["b2","c2"],["b2"],["c2"],[]]}。請依 [points, pair_witness_rows, Hausdorff, certificate] 欄序回答。

查看答案與解釋([a2, b2, c2], [[a2, b2, [[a2, c2], [b2]]], [a2, c2, [[a2, b2], [c2]]], [b2, c2, [[a2, b2], [c2]]]], 是, all_distinct_pairs_exhaustively_separated)

Wave6第五層核對=([a2, b2, c2], [[a2, b2, [[a2, c2], [b2]]], [a2, c2, [[a2, b2], [c2]]], [b2, c2, [[a2, b2], [c2]]]], 是, all_distinct_pairs_exhaustively_separated)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0028/)

Hausdorff空間 · qf-mod42-hausdorff-full-audit · candidate





## 29. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-full-audit；資料={"points":["a3","b3","c3"],"topology":[["a3","b3","c3"],["a3","b3"],["a3","c3"],["a3"],["b3","c3"],["b3"],["c3"],[]]}。請依 [points, pair_witness_rows, Hausdorff, certificate] 欄序回答。

查看答案與解釋([a3, b3, c3], [[a3, b3, [[a3, c3], [b3]]], [a3, c3, [[a3, b3], [c3]]], [b3, c3, [[a3, b3], [c3]]]], 是, all_distinct_pairs_exhaustively_separated)

Wave6第五層核對=([a3, b3, c3], [[a3, b3, [[a3, c3], [b3]]], [a3, c3, [[a3, b3], [c3]]], [b3, c3, [[a3, b3], [c3]]]], 是, all_distinct_pairs_exhaustively_separated)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0029/)

Hausdorff空間 · qf-mod42-hausdorff-full-audit · candidate





## 30. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-full-audit；資料={"points":["a4","b4","c4"],"topology":[["a4","b4","c4"],["a4","b4"],["a4","c4"],["a4"],["b4","c4"],["b4"],["c4"],[]]}。請依 [points, pair_witness_rows, Hausdorff, certificate] 欄序回答。

查看答案與解釋([a4, b4, c4], [[a4, b4, [[a4, c4], [b4]]], [a4, c4, [[a4, b4], [c4]]], [b4, c4, [[a4, b4], [c4]]]], 是, all_distinct_pairs_exhaustively_separated)

Wave6第五層核對=([a4, b4, c4], [[a4, b4, [[a4, c4], [b4]]], [a4, c4, [[a4, b4], [c4]]], [b4, c4, [[a4, b4], [c4]]]], 是, all_distinct_pairs_exhaustively_separated)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0030/)

Hausdorff空間 · qf-mod42-hausdorff-full-audit · candidate





## 31. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-full-audit；資料={"points":["a5","b5","c5"],"topology":[["a5","b5","c5"],["a5","b5"],["a5","c5"],["a5"],["b5","c5"],["b5"],["c5"],[]]}。請依 [points, pair_witness_rows, Hausdorff, certificate] 欄序回答。

查看答案與解釋([a5, b5, c5], [[a5, b5, [[a5, c5], [b5]]], [a5, c5, [[a5, b5], [c5]]], [b5, c5, [[a5, b5], [c5]]]], 是, all_distinct_pairs_exhaustively_separated)

Wave6第五層核對=([a5, b5, c5], [[a5, b5, [[a5, c5], [b5]]], [a5, c5, [[a5, b5], [c5]]], [b5, c5, [[a5, b5], [c5]]]], 是, all_distinct_pairs_exhaustively_separated)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0031/)

Hausdorff空間 · qf-mod42-hausdorff-full-audit · candidate





## 32. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-full-audit；資料={"points":["a6","b6","c6"],"topology":[["a6","b6","c6"],["a6","b6"],["a6","c6"],["a6"],["b6","c6"],["b6"],["c6"],[]]}。請依 [points, pair_witness_rows, Hausdorff, certificate] 欄序回答。

查看答案與解釋([a6, b6, c6], [[a6, b6, [[a6, c6], [b6]]], [a6, c6, [[a6, b6], [c6]]], [b6, c6, [[a6, b6], [c6]]]], 是, all_distinct_pairs_exhaustively_separated)

Wave6第五層核對=([a6, b6, c6], [[a6, b6, [[a6, c6], [b6]]], [a6, c6, [[a6, b6], [c6]]], [b6, c6, [[a6, b6], [c6]]]], 是, all_distinct_pairs_exhaustively_separated)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0032/)

Hausdorff空間 · qf-mod42-hausdorff-full-audit · candidate





## 33. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-full-audit；資料={"points":["a7","b7","c7"],"topology":[["a7","b7","c7"],["a7","b7"],["a7","c7"],["a7"],["b7","c7"],["b7"],["c7"],[]]}。請依 [points, pair_witness_rows, Hausdorff, certificate] 欄序回答。

查看答案與解釋([a7, b7, c7], [[a7, b7, [[a7, c7], [b7]]], [a7, c7, [[a7, b7], [c7]]], [b7, c7, [[a7, b7], [c7]]]], 是, all_distinct_pairs_exhaustively_separated)

Wave6第五層核對=([a7, b7, c7], [[a7, b7, [[a7, c7], [b7]]], [a7, c7, [[a7, b7], [c7]]], [b7, c7, [[a7, b7], [c7]]]], 是, all_distinct_pairs_exhaustively_separated)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0033/)

Hausdorff空間 · qf-mod42-hausdorff-full-audit · candidate





## 34. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-full-audit；資料={"points":["a8","b8","c8"],"topology":[["a8","b8","c8"],["a8","b8"],["a8","c8"],["a8"],["b8","c8"],["b8"],["c8"],[]]}。請依 [points, pair_witness_rows, Hausdorff, certificate] 欄序回答。

查看答案與解釋([a8, b8, c8], [[a8, b8, [[a8, c8], [b8]]], [a8, c8, [[a8, b8], [c8]]], [b8, c8, [[a8, b8], [c8]]]], 是, all_distinct_pairs_exhaustively_separated)

Wave6第五層核對=([a8, b8, c8], [[a8, b8, [[a8, c8], [b8]]], [a8, c8, [[a8, b8], [c8]]], [b8, c8, [[a8, b8], [c8]]]], 是, all_distinct_pairs_exhaustively_separated)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0034/)

Hausdorff空間 · qf-mod42-hausdorff-full-audit · candidate





## 35. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-full-audit；資料={"points":["a9","b9","c9"],"topology":[["a9","b9","c9"],["a9","b9"],["a9","c9"],["a9"],["b9","c9"],["b9"],["c9"],[]]}。請依 [points, pair_witness_rows, Hausdorff, certificate] 欄序回答。

查看答案與解釋([a9, b9, c9], [[a9, b9, [[a9, c9], [b9]]], [a9, c9, [[a9, b9], [c9]]], [b9, c9, [[a9, b9], [c9]]]], 是, all_distinct_pairs_exhaustively_separated)

Wave6第五層核對=([a9, b9, c9], [[a9, b9, [[a9, c9], [b9]]], [a9, c9, [[a9, b9], [c9]]], [b9, c9, [[a9, b9], [c9]]]], 是, all_distinct_pairs_exhaustively_separated)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0035/)

Hausdorff空間 · qf-mod42-hausdorff-full-audit · candidate





## 36. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-full-audit；資料={"points":["a10","b10","c10"],"topology":[["a10","b10","c10"],["a10","b10"],["a10","c10"],["a10"],["b10","c10"],["b10"],["c10"],[]]}。請依 [points, pair_witness_rows, Hausdorff, certificate] 欄序回答。

查看答案與解釋([a10, b10, c10], [[a10, b10, [[a10, c10], [b10]]], [a10, c10, [[a10, b10], [c10]]], [b10, c10, [[a10, b10], [c10]]]], 是, all_distinct_pairs_exhaustively_separated)

Wave6第五層核對=([a10, b10, c10], [[a10, b10, [[a10, c10], [b10]]], [a10, c10, [[a10, b10], [c10]]], [b10, c10, [[a10, b10], [c10]]]], 是, all_distinct_pairs_exhaustively_separated)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0036/)

Hausdorff空間 · qf-mod42-hausdorff-full-audit · candidate





## 37. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-full-audit；資料={"points":["a11","b11","c11"],"topology":[["a11","b11","c11"],["a11","b11"],["a11","c11"],["a11"],["b11","c11"],["b11"],["c11"],[]]}。請依 [points, pair_witness_rows, Hausdorff, certificate] 欄序回答。

查看答案與解釋([a11, b11, c11], [[a11, b11, [[a11, c11], [b11]]], [a11, c11, [[a11, b11], [c11]]], [b11, c11, [[a11, b11], [c11]]]], 是, all_distinct_pairs_exhaustively_separated)

Wave6第五層核對=([a11, b11, c11], [[a11, b11, [[a11, c11], [b11]]], [a11, c11, [[a11, b11], [c11]]], [b11, c11, [[a11, b11], [c11]]]], 是, all_distinct_pairs_exhaustively_separated)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0037/)

Hausdorff空間 · qf-mod42-hausdorff-full-audit · candidate





## 38. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-full-audit；資料={"points":["a12","b12","c12"],"topology":[["a12","b12","c12"],["a12","b12"],["a12","c12"],["a12"],["b12","c12"],["b12"],["c12"],[]]}。請依 [points, pair_witness_rows, Hausdorff, certificate] 欄序回答。

查看答案與解釋([a12, b12, c12], [[a12, b12, [[a12, c12], [b12]]], [a12, c12, [[a12, b12], [c12]]], [b12, c12, [[a12, b12], [c12]]]], 是, all_distinct_pairs_exhaustively_separated)

Wave6第五層核對=([a12, b12, c12], [[a12, b12, [[a12, c12], [b12]]], [a12, c12, [[a12, b12], [c12]]], [b12, c12, [[a12, b12], [c12]]]], 是, all_distinct_pairs_exhaustively_separated)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0038/)

Hausdorff空間 · qf-mod42-hausdorff-full-audit · candidate





## 39. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-full-audit；資料={"points":["a13","b13","c13"],"topology":[["a13","b13","c13"],["a13","b13"],["a13","c13"],["a13"],["b13","c13"],["b13"],["c13"],[]]}。請依 [points, pair_witness_rows, Hausdorff, certificate] 欄序回答。

查看答案與解釋([a13, b13, c13], [[a13, b13, [[a13, c13], [b13]]], [a13, c13, [[a13, b13], [c13]]], [b13, c13, [[a13, b13], [c13]]]], 是, all_distinct_pairs_exhaustively_separated)

Wave6第五層核對=([a13, b13, c13], [[a13, b13, [[a13, c13], [b13]]], [a13, c13, [[a13, b13], [c13]]], [b13, c13, [[a13, b13], [c13]]]], 是, all_distinct_pairs_exhaustively_separated)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0039/)

Hausdorff空間 · qf-mod42-hausdorff-full-audit · candidate





## 40. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-full-audit；資料={"points":["a14","b14","c14"],"topology":[["a14","b14","c14"],["a14","b14"],["a14","c14"],["a14"],["b14","c14"],["b14"],["c14"],[]]}。請依 [points, pair_witness_rows, Hausdorff, certificate] 欄序回答。

查看答案與解釋([a14, b14, c14], [[a14, b14, [[a14, c14], [b14]]], [a14, c14, [[a14, b14], [c14]]], [b14, c14, [[a14, b14], [c14]]]], 是, all_distinct_pairs_exhaustively_separated)

Wave6第五層核對=([a14, b14, c14], [[a14, b14, [[a14, c14], [b14]]], [a14, c14, [[a14, b14], [c14]]], [b14, c14, [[a14, b14], [c14]]]], 是, all_distinct_pairs_exhaustively_separated)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0040/)

Hausdorff空間 · qf-mod42-hausdorff-full-audit · candidate





## 41. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-full-audit；資料={"points":["a15","b15","c15"],"topology":[["a15","b15","c15"],["a15","b15"],["a15","c15"],["a15"],["b15","c15"],["b15"],["c15"],[]]}。請依 [points, pair_witness_rows, Hausdorff, certificate] 欄序回答。

查看答案與解釋([a15, b15, c15], [[a15, b15, [[a15, c15], [b15]]], [a15, c15, [[a15, b15], [c15]]], [b15, c15, [[a15, b15], [c15]]]], 是, all_distinct_pairs_exhaustively_separated)

Wave6第五層核對=([a15, b15, c15], [[a15, b15, [[a15, c15], [b15]]], [a15, c15, [[a15, b15], [c15]]], [b15, c15, [[a15, b15], [c15]]]], 是, all_distinct_pairs_exhaustively_separated)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0041/)

Hausdorff空間 · qf-mod42-hausdorff-full-audit · candidate





## 42. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-full-audit；資料={"points":["a16","b16","c16"],"topology":[["a16","b16","c16"],["a16","b16"],["a16","c16"],["a16"],["b16","c16"],["b16"],["c16"],[]]}。請依 [points, pair_witness_rows, Hausdorff, certificate] 欄序回答。

查看答案與解釋([a16, b16, c16], [[a16, b16, [[a16, c16], [b16]]], [a16, c16, [[a16, b16], [c16]]], [b16, c16, [[a16, b16], [c16]]]], 是, all_distinct_pairs_exhaustively_separated)

Wave6第五層核對=([a16, b16, c16], [[a16, b16, [[a16, c16], [b16]]], [a16, c16, [[a16, b16], [c16]]], [b16, c16, [[a16, b16], [c16]]]], 是, all_distinct_pairs_exhaustively_separated)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0042/)

Hausdorff空間 · qf-mod42-hausdorff-full-audit · candidate





## 43. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-full-audit；資料={"points":["a17","b17","c17"],"topology":[["a17","b17","c17"],["a17","b17"],["a17","c17"],["a17"],["b17","c17"],["b17"],["c17"],[]]}。請依 [points, pair_witness_rows, Hausdorff, certificate] 欄序回答。

查看答案與解釋([a17, b17, c17], [[a17, b17, [[a17, c17], [b17]]], [a17, c17, [[a17, b17], [c17]]], [b17, c17, [[a17, b17], [c17]]]], 是, all_distinct_pairs_exhaustively_separated)

Wave6第五層核對=([a17, b17, c17], [[a17, b17, [[a17, c17], [b17]]], [a17, c17, [[a17, b17], [c17]]], [b17, c17, [[a17, b17], [c17]]]], 是, all_distinct_pairs_exhaustively_separated)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0043/)

Hausdorff空間 · qf-mod42-hausdorff-full-audit · candidate





## 44. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-full-audit；資料={"points":["a18","b18","c18"],"topology":[["a18","b18","c18"],["a18","b18"],["a18","c18"],["a18"],["b18","c18"],["b18"],["c18"],[]]}。請依 [points, pair_witness_rows, Hausdorff, certificate] 欄序回答。

查看答案與解釋([a18, b18, c18], [[a18, b18, [[a18, c18], [b18]]], [a18, c18, [[a18, b18], [c18]]], [b18, c18, [[a18, b18], [c18]]]], 是, all_distinct_pairs_exhaustively_separated)

Wave6第五層核對=([a18, b18, c18], [[a18, b18, [[a18, c18], [b18]]], [a18, c18, [[a18, b18], [c18]]], [b18, c18, [[a18, b18], [c18]]]], 是, all_distinct_pairs_exhaustively_separated)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0044/)

Hausdorff空間 · qf-mod42-hausdorff-full-audit · candidate





## 45. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-full-audit；資料={"points":["a19","b19","c19"],"topology":[["a19","b19","c19"],["a19","b19"],["a19","c19"],["a19"],["b19","c19"],["b19"],["c19"],[]]}。請依 [points, pair_witness_rows, Hausdorff, certificate] 欄序回答。

查看答案與解釋([a19, b19, c19], [[a19, b19, [[a19, c19], [b19]]], [a19, c19, [[a19, b19], [c19]]], [b19, c19, [[a19, b19], [c19]]]], 是, all_distinct_pairs_exhaustively_separated)

Wave6第五層核對=([a19, b19, c19], [[a19, b19, [[a19, c19], [b19]]], [a19, c19, [[a19, b19], [c19]]], [b19, c19, [[a19, b19], [c19]]]], 是, all_distinct_pairs_exhaustively_separated)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0045/)

Hausdorff空間 · qf-mod42-hausdorff-full-audit · candidate





## 46. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-full-audit；資料={"points":["a20","b20","c20"],"topology":[["a20","b20","c20"],["a20","b20"],["a20","c20"],["a20"],["b20","c20"],["b20"],["c20"],[]]}。請依 [points, pair_witness_rows, Hausdorff, certificate] 欄序回答。

查看答案與解釋([a20, b20, c20], [[a20, b20, [[a20, c20], [b20]]], [a20, c20, [[a20, b20], [c20]]], [b20, c20, [[a20, b20], [c20]]]], 是, all_distinct_pairs_exhaustively_separated)

Wave6第五層核對=([a20, b20, c20], [[a20, b20, [[a20, c20], [b20]]], [a20, c20, [[a20, b20], [c20]]], [b20, c20, [[a20, b20], [c20]]]], 是, all_distinct_pairs_exhaustively_separated)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0046/)

Hausdorff空間 · qf-mod42-hausdorff-full-audit · candidate





## 47. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-full-audit；資料={"points":["a21","b21","c21"],"topology":[["a21","b21","c21"],["a21","b21"],["a21","c21"],["a21"],["b21","c21"],["b21"],["c21"],[]]}。請依 [points, pair_witness_rows, Hausdorff, certificate] 欄序回答。

查看答案與解釋([a21, b21, c21], [[a21, b21, [[a21, c21], [b21]]], [a21, c21, [[a21, b21], [c21]]], [b21, c21, [[a21, b21], [c21]]]], 是, all_distinct_pairs_exhaustively_separated)

Wave6第五層核對=([a21, b21, c21], [[a21, b21, [[a21, c21], [b21]]], [a21, c21, [[a21, b21], [c21]]], [b21, c21, [[a21, b21], [c21]]]], 是, all_distinct_pairs_exhaustively_separated)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0047/)

Hausdorff空間 · qf-mod42-hausdorff-full-audit · candidate





## 48. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-full-audit；資料={"points":["a22","b22","c22"],"topology":[["a22","b22","c22"],["a22","b22"],["a22","c22"],["a22"],["b22","c22"],["b22"],["c22"],[]]}。請依 [points, pair_witness_rows, Hausdorff, certificate] 欄序回答。

查看答案與解釋([a22, b22, c22], [[a22, b22, [[a22, c22], [b22]]], [a22, c22, [[a22, b22], [c22]]], [b22, c22, [[a22, b22], [c22]]]], 是, all_distinct_pairs_exhaustively_separated)

Wave6第五層核對=([a22, b22, c22], [[a22, b22, [[a22, c22], [b22]]], [a22, c22, [[a22, b22], [c22]]], [b22, c22, [[a22, b22], [c22]]]], 是, all_distinct_pairs_exhaustively_separated)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0048/)

Hausdorff空間 · qf-mod42-hausdorff-full-audit · candidate





## 49. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-full-audit；資料={"points":["a23","b23","c23"],"topology":[["a23","b23","c23"],["a23","b23"],["a23","c23"],["a23"],["b23","c23"],["b23"],["c23"],[]]}。請依 [points, pair_witness_rows, Hausdorff, certificate] 欄序回答。

查看答案與解釋([a23, b23, c23], [[a23, b23, [[a23, c23], [b23]]], [a23, c23, [[a23, b23], [c23]]], [b23, c23, [[a23, b23], [c23]]]], 是, all_distinct_pairs_exhaustively_separated)

Wave6第五層核對=([a23, b23, c23], [[a23, b23, [[a23, c23], [b23]]], [a23, c23, [[a23, b23], [c23]]], [b23, c23, [[a23, b23], [c23]]]], 是, all_distinct_pairs_exhaustively_separated)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0049/)

Hausdorff空間 · qf-mod42-hausdorff-full-audit · candidate





## 50. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-full-audit；資料={"points":["a24","b24","c24"],"topology":[["a24","b24","c24"],["a24","b24"],["a24","c24"],["a24"],["b24","c24"],["b24"],["c24"],[]]}。請依 [points, pair_witness_rows, Hausdorff, certificate] 欄序回答。

查看答案與解釋([a24, b24, c24], [[a24, b24, [[a24, c24], [b24]]], [a24, c24, [[a24, b24], [c24]]], [b24, c24, [[a24, b24], [c24]]]], 是, all_distinct_pairs_exhaustively_separated)

Wave6第五層核對=([a24, b24, c24], [[a24, b24, [[a24, c24], [b24]]], [a24, c24, [[a24, b24], [c24]]], [b24, c24, [[a24, b24], [c24]]]], 是, all_distinct_pairs_exhaustively_separated)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0050/)

Hausdorff空間 · qf-mod42-hausdorff-full-audit · candidate





## 51. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-inseparable-pair；資料={"points":["a0","b0","c0"],"topology":[["a0","b0","c0"],["a0","b0"],["a0"],[]],"x":"a0","y":"b0"}。請依 [x, y, witness_or_null, separated, boundary] 欄序回答。

查看答案與解釋(a0, b0, null, 否, one_failed_distinct_pair_proves_non_Hausdorff)

Wave6第五層核對=(a0, b0, null, 否, one_failed_distinct_pair_proves_non_Hausdorff)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0051/)

Hausdorff空間 · qf-mod42-hausdorff-inseparable-pair · candidate





## 52. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-inseparable-pair；資料={"points":["a1","b1","c1"],"topology":[["a1","b1","c1"],["a1","b1"],["a1"],[]],"x":"a1","y":"b1"}。請依 [x, y, witness_or_null, separated, boundary] 欄序回答。

查看答案與解釋(a1, b1, null, 否, one_failed_distinct_pair_proves_non_Hausdorff)

Wave6第五層核對=(a1, b1, null, 否, one_failed_distinct_pair_proves_non_Hausdorff)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0052/)

Hausdorff空間 · qf-mod42-hausdorff-inseparable-pair · candidate





## 53. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-inseparable-pair；資料={"points":["a2","b2","c2"],"topology":[["a2","b2","c2"],["a2","b2"],["a2"],[]],"x":"a2","y":"b2"}。請依 [x, y, witness_or_null, separated, boundary] 欄序回答。

查看答案與解釋(a2, b2, null, 否, one_failed_distinct_pair_proves_non_Hausdorff)

Wave6第五層核對=(a2, b2, null, 否, one_failed_distinct_pair_proves_non_Hausdorff)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0053/)

Hausdorff空間 · qf-mod42-hausdorff-inseparable-pair · candidate





## 54. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-inseparable-pair；資料={"points":["a3","b3","c3"],"topology":[["a3","b3","c3"],["a3","b3"],["a3"],[]],"x":"a3","y":"b3"}。請依 [x, y, witness_or_null, separated, boundary] 欄序回答。

查看答案與解釋(a3, b3, null, 否, one_failed_distinct_pair_proves_non_Hausdorff)

Wave6第五層核對=(a3, b3, null, 否, one_failed_distinct_pair_proves_non_Hausdorff)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0054/)

Hausdorff空間 · qf-mod42-hausdorff-inseparable-pair · candidate





## 55. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-inseparable-pair；資料={"points":["a4","b4","c4"],"topology":[["a4","b4","c4"],["a4","b4"],["a4"],[]],"x":"a4","y":"b4"}。請依 [x, y, witness_or_null, separated, boundary] 欄序回答。

查看答案與解釋(a4, b4, null, 否, one_failed_distinct_pair_proves_non_Hausdorff)

Wave6第五層核對=(a4, b4, null, 否, one_failed_distinct_pair_proves_non_Hausdorff)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0055/)

Hausdorff空間 · qf-mod42-hausdorff-inseparable-pair · candidate





## 56. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-inseparable-pair；資料={"points":["a5","b5","c5"],"topology":[["a5","b5","c5"],["a5","b5"],["a5"],[]],"x":"a5","y":"b5"}。請依 [x, y, witness_or_null, separated, boundary] 欄序回答。

查看答案與解釋(a5, b5, null, 否, one_failed_distinct_pair_proves_non_Hausdorff)

Wave6第五層核對=(a5, b5, null, 否, one_failed_distinct_pair_proves_non_Hausdorff)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0056/)

Hausdorff空間 · qf-mod42-hausdorff-inseparable-pair · candidate





## 57. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-inseparable-pair；資料={"points":["a6","b6","c6"],"topology":[["a6","b6","c6"],["a6","b6"],["a6"],[]],"x":"a6","y":"b6"}。請依 [x, y, witness_or_null, separated, boundary] 欄序回答。

查看答案與解釋(a6, b6, null, 否, one_failed_distinct_pair_proves_non_Hausdorff)

Wave6第五層核對=(a6, b6, null, 否, one_failed_distinct_pair_proves_non_Hausdorff)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0057/)

Hausdorff空間 · qf-mod42-hausdorff-inseparable-pair · candidate





## 58. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-inseparable-pair；資料={"points":["a7","b7","c7"],"topology":[["a7","b7","c7"],["a7","b7"],["a7"],[]],"x":"a7","y":"b7"}。請依 [x, y, witness_or_null, separated, boundary] 欄序回答。

查看答案與解釋(a7, b7, null, 否, one_failed_distinct_pair_proves_non_Hausdorff)

Wave6第五層核對=(a7, b7, null, 否, one_failed_distinct_pair_proves_non_Hausdorff)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0058/)

Hausdorff空間 · qf-mod42-hausdorff-inseparable-pair · candidate





## 59. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-inseparable-pair；資料={"points":["a8","b8","c8"],"topology":[["a8","b8","c8"],["a8","b8"],["a8"],[]],"x":"a8","y":"b8"}。請依 [x, y, witness_or_null, separated, boundary] 欄序回答。

查看答案與解釋(a8, b8, null, 否, one_failed_distinct_pair_proves_non_Hausdorff)

Wave6第五層核對=(a8, b8, null, 否, one_failed_distinct_pair_proves_non_Hausdorff)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0059/)

Hausdorff空間 · qf-mod42-hausdorff-inseparable-pair · candidate





## 60. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-inseparable-pair；資料={"points":["a9","b9","c9"],"topology":[["a9","b9","c9"],["a9","b9"],["a9"],[]],"x":"a9","y":"b9"}。請依 [x, y, witness_or_null, separated, boundary] 欄序回答。

查看答案與解釋(a9, b9, null, 否, one_failed_distinct_pair_proves_non_Hausdorff)

Wave6第五層核對=(a9, b9, null, 否, one_failed_distinct_pair_proves_non_Hausdorff)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0060/)

Hausdorff空間 · qf-mod42-hausdorff-inseparable-pair · candidate





## 61. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-inseparable-pair；資料={"points":["a10","b10","c10"],"topology":[["a10","b10","c10"],["a10","b10"],["a10"],[]],"x":"a10","y":"b10"}。請依 [x, y, witness_or_null, separated, boundary] 欄序回答。

查看答案與解釋(a10, b10, null, 否, one_failed_distinct_pair_proves_non_Hausdorff)

Wave6第五層核對=(a10, b10, null, 否, one_failed_distinct_pair_proves_non_Hausdorff)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0061/)

Hausdorff空間 · qf-mod42-hausdorff-inseparable-pair · candidate





## 62. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-inseparable-pair；資料={"points":["a11","b11","c11"],"topology":[["a11","b11","c11"],["a11","b11"],["a11"],[]],"x":"a11","y":"b11"}。請依 [x, y, witness_or_null, separated, boundary] 欄序回答。

查看答案與解釋(a11, b11, null, 否, one_failed_distinct_pair_proves_non_Hausdorff)

Wave6第五層核對=(a11, b11, null, 否, one_failed_distinct_pair_proves_non_Hausdorff)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0062/)

Hausdorff空間 · qf-mod42-hausdorff-inseparable-pair · candidate





## 63. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-inseparable-pair；資料={"points":["a12","b12","c12"],"topology":[["a12","b12","c12"],["a12","b12"],["a12"],[]],"x":"a12","y":"b12"}。請依 [x, y, witness_or_null, separated, boundary] 欄序回答。

查看答案與解釋(a12, b12, null, 否, one_failed_distinct_pair_proves_non_Hausdorff)

Wave6第五層核對=(a12, b12, null, 否, one_failed_distinct_pair_proves_non_Hausdorff)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0063/)

Hausdorff空間 · qf-mod42-hausdorff-inseparable-pair · candidate





## 64. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-inseparable-pair；資料={"points":["a13","b13","c13"],"topology":[["a13","b13","c13"],["a13","b13"],["a13"],[]],"x":"a13","y":"b13"}。請依 [x, y, witness_or_null, separated, boundary] 欄序回答。

查看答案與解釋(a13, b13, null, 否, one_failed_distinct_pair_proves_non_Hausdorff)

Wave6第五層核對=(a13, b13, null, 否, one_failed_distinct_pair_proves_non_Hausdorff)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0064/)

Hausdorff空間 · qf-mod42-hausdorff-inseparable-pair · candidate





## 65. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-inseparable-pair；資料={"points":["a14","b14","c14"],"topology":[["a14","b14","c14"],["a14","b14"],["a14"],[]],"x":"a14","y":"b14"}。請依 [x, y, witness_or_null, separated, boundary] 欄序回答。

查看答案與解釋(a14, b14, null, 否, one_failed_distinct_pair_proves_non_Hausdorff)

Wave6第五層核對=(a14, b14, null, 否, one_failed_distinct_pair_proves_non_Hausdorff)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0065/)

Hausdorff空間 · qf-mod42-hausdorff-inseparable-pair · candidate





## 66. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-inseparable-pair；資料={"points":["a15","b15","c15"],"topology":[["a15","b15","c15"],["a15","b15"],["a15"],[]],"x":"a15","y":"b15"}。請依 [x, y, witness_or_null, separated, boundary] 欄序回答。

查看答案與解釋(a15, b15, null, 否, one_failed_distinct_pair_proves_non_Hausdorff)

Wave6第五層核對=(a15, b15, null, 否, one_failed_distinct_pair_proves_non_Hausdorff)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0066/)

Hausdorff空間 · qf-mod42-hausdorff-inseparable-pair · candidate





## 67. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-inseparable-pair；資料={"points":["a16","b16","c16"],"topology":[["a16","b16","c16"],["a16","b16"],["a16"],[]],"x":"a16","y":"b16"}。請依 [x, y, witness_or_null, separated, boundary] 欄序回答。

查看答案與解釋(a16, b16, null, 否, one_failed_distinct_pair_proves_non_Hausdorff)

Wave6第五層核對=(a16, b16, null, 否, one_failed_distinct_pair_proves_non_Hausdorff)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0067/)

Hausdorff空間 · qf-mod42-hausdorff-inseparable-pair · candidate





## 68. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-inseparable-pair；資料={"points":["a17","b17","c17"],"topology":[["a17","b17","c17"],["a17","b17"],["a17"],[]],"x":"a17","y":"b17"}。請依 [x, y, witness_or_null, separated, boundary] 欄序回答。

查看答案與解釋(a17, b17, null, 否, one_failed_distinct_pair_proves_non_Hausdorff)

Wave6第五層核對=(a17, b17, null, 否, one_failed_distinct_pair_proves_non_Hausdorff)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0068/)

Hausdorff空間 · qf-mod42-hausdorff-inseparable-pair · candidate





## 69. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-inseparable-pair；資料={"points":["a18","b18","c18"],"topology":[["a18","b18","c18"],["a18","b18"],["a18"],[]],"x":"a18","y":"b18"}。請依 [x, y, witness_or_null, separated, boundary] 欄序回答。

查看答案與解釋(a18, b18, null, 否, one_failed_distinct_pair_proves_non_Hausdorff)

Wave6第五層核對=(a18, b18, null, 否, one_failed_distinct_pair_proves_non_Hausdorff)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0069/)

Hausdorff空間 · qf-mod42-hausdorff-inseparable-pair · candidate





## 70. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-inseparable-pair；資料={"points":["a19","b19","c19"],"topology":[["a19","b19","c19"],["a19","b19"],["a19"],[]],"x":"a19","y":"b19"}。請依 [x, y, witness_or_null, separated, boundary] 欄序回答。

查看答案與解釋(a19, b19, null, 否, one_failed_distinct_pair_proves_non_Hausdorff)

Wave6第五層核對=(a19, b19, null, 否, one_failed_distinct_pair_proves_non_Hausdorff)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0070/)

Hausdorff空間 · qf-mod42-hausdorff-inseparable-pair · candidate





## 71. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-inseparable-pair；資料={"points":["a20","b20","c20"],"topology":[["a20","b20","c20"],["a20","b20"],["a20"],[]],"x":"a20","y":"b20"}。請依 [x, y, witness_or_null, separated, boundary] 欄序回答。

查看答案與解釋(a20, b20, null, 否, one_failed_distinct_pair_proves_non_Hausdorff)

Wave6第五層核對=(a20, b20, null, 否, one_failed_distinct_pair_proves_non_Hausdorff)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0071/)

Hausdorff空間 · qf-mod42-hausdorff-inseparable-pair · candidate





## 72. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-inseparable-pair；資料={"points":["a21","b21","c21"],"topology":[["a21","b21","c21"],["a21","b21"],["a21"],[]],"x":"a21","y":"b21"}。請依 [x, y, witness_or_null, separated, boundary] 欄序回答。

查看答案與解釋(a21, b21, null, 否, one_failed_distinct_pair_proves_non_Hausdorff)

Wave6第五層核對=(a21, b21, null, 否, one_failed_distinct_pair_proves_non_Hausdorff)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0072/)

Hausdorff空間 · qf-mod42-hausdorff-inseparable-pair · candidate





## 73. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-inseparable-pair；資料={"points":["a22","b22","c22"],"topology":[["a22","b22","c22"],["a22","b22"],["a22"],[]],"x":"a22","y":"b22"}。請依 [x, y, witness_or_null, separated, boundary] 欄序回答。

查看答案與解釋(a22, b22, null, 否, one_failed_distinct_pair_proves_non_Hausdorff)

Wave6第五層核對=(a22, b22, null, 否, one_failed_distinct_pair_proves_non_Hausdorff)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0073/)

Hausdorff空間 · qf-mod42-hausdorff-inseparable-pair · candidate





## 74. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-inseparable-pair；資料={"points":["a23","b23","c23"],"topology":[["a23","b23","c23"],["a23","b23"],["a23"],[]],"x":"a23","y":"b23"}。請依 [x, y, witness_or_null, separated, boundary] 欄序回答。

查看答案與解釋(a23, b23, null, 否, one_failed_distinct_pair_proves_non_Hausdorff)

Wave6第五層核對=(a23, b23, null, 否, one_failed_distinct_pair_proves_non_Hausdorff)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0074/)

Hausdorff空間 · qf-mod42-hausdorff-inseparable-pair · candidate





## 75. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-inseparable-pair；資料={"points":["a24","b24","c24"],"topology":[["a24","b24","c24"],["a24","b24"],["a24"],[]],"x":"a24","y":"b24"}。請依 [x, y, witness_or_null, separated, boundary] 欄序回答。

查看答案與解釋(a24, b24, null, 否, one_failed_distinct_pair_proves_non_Hausdorff)

Wave6第五層核對=(a24, b24, null, 否, one_failed_distinct_pair_proves_non_Hausdorff)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0075/)

Hausdorff空間 · qf-mod42-hausdorff-inseparable-pair · candidate





## 76. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-sampled-boundary；資料={"points":["a0","b0","c0"],"topology":[["a0","b0","c0"],["a0","b0"],["a0","c0"],["a0"],["c0"],[]],"sampled_pairs":[["c0","a0"]]}。請依 [sampled_pair_rows, all_sampled_separated, sample_count, total_pair_count, general_sample_certificate, boundary] 欄序回答。

固定的否是不從抽樣聲稱一般空間或未核點對的Hausdorff性；不否定前面的分離旗標。若實際已覆蓋全部有限點對，完整性仍須另行明示。

查看答案與解釋([[c0, a0, [[c0], [a0, b0]]]], 是, 1, 3, 否, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)

Wave6第五層核對=([[c0, a0, [[c0], [a0, b0]]]], 是, 1, 3, 否, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0076/)

Hausdorff空間 · qf-mod42-hausdorff-sampled-boundary · candidate





## 77. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-sampled-boundary；資料={"points":["a1","b1","c1"],"topology":[["a1","b1","c1"],["a1","b1"],["a1","c1"],["a1"],["c1"],[]],"sampled_pairs":[["c1","a1"]]}。請依 [sampled_pair_rows, all_sampled_separated, sample_count, total_pair_count, general_sample_certificate, boundary] 欄序回答。

固定的否是不從抽樣聲稱一般空間或未核點對的Hausdorff性；不否定前面的分離旗標。若實際已覆蓋全部有限點對，完整性仍須另行明示。

查看答案與解釋([[c1, a1, [[c1], [a1, b1]]]], 是, 1, 3, 否, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)

Wave6第五層核對=([[c1, a1, [[c1], [a1, b1]]]], 是, 1, 3, 否, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0077/)

Hausdorff空間 · qf-mod42-hausdorff-sampled-boundary · candidate





## 78. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-sampled-boundary；資料={"points":["a2","b2","c2"],"topology":[["a2","b2","c2"],["a2","b2"],["a2","c2"],["a2"],["c2"],[]],"sampled_pairs":[["c2","a2"]]}。請依 [sampled_pair_rows, all_sampled_separated, sample_count, total_pair_count, general_sample_certificate, boundary] 欄序回答。

固定的否是不從抽樣聲稱一般空間或未核點對的Hausdorff性；不否定前面的分離旗標。若實際已覆蓋全部有限點對，完整性仍須另行明示。

查看答案與解釋([[c2, a2, [[c2], [a2, b2]]]], 是, 1, 3, 否, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)

Wave6第五層核對=([[c2, a2, [[c2], [a2, b2]]]], 是, 1, 3, 否, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0078/)

Hausdorff空間 · qf-mod42-hausdorff-sampled-boundary · candidate





## 79. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-sampled-boundary；資料={"points":["a3","b3","c3"],"topology":[["a3","b3","c3"],["a3","b3"],["a3","c3"],["a3"],["c3"],[]],"sampled_pairs":[["c3","a3"]]}。請依 [sampled_pair_rows, all_sampled_separated, sample_count, total_pair_count, general_sample_certificate, boundary] 欄序回答。

固定的否是不從抽樣聲稱一般空間或未核點對的Hausdorff性；不否定前面的分離旗標。若實際已覆蓋全部有限點對，完整性仍須另行明示。

查看答案與解釋([[c3, a3, [[c3], [a3, b3]]]], 是, 1, 3, 否, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)

Wave6第五層核對=([[c3, a3, [[c3], [a3, b3]]]], 是, 1, 3, 否, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0079/)

Hausdorff空間 · qf-mod42-hausdorff-sampled-boundary · candidate





## 80. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-sampled-boundary；資料={"points":["a4","b4","c4"],"topology":[["a4","b4","c4"],["a4","b4"],["a4","c4"],["a4"],["c4"],[]],"sampled_pairs":[["c4","a4"]]}。請依 [sampled_pair_rows, all_sampled_separated, sample_count, total_pair_count, general_sample_certificate, boundary] 欄序回答。

固定的否是不從抽樣聲稱一般空間或未核點對的Hausdorff性；不否定前面的分離旗標。若實際已覆蓋全部有限點對，完整性仍須另行明示。

查看答案與解釋([[c4, a4, [[c4], [a4, b4]]]], 是, 1, 3, 否, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)

Wave6第五層核對=([[c4, a4, [[c4], [a4, b4]]]], 是, 1, 3, 否, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0080/)

Hausdorff空間 · qf-mod42-hausdorff-sampled-boundary · candidate





## 81. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-sampled-boundary；資料={"points":["a5","b5","c5"],"topology":[["a5","b5","c5"],["a5","b5"],["a5","c5"],["a5"],["c5"],[]],"sampled_pairs":[["c5","a5"]]}。請依 [sampled_pair_rows, all_sampled_separated, sample_count, total_pair_count, general_sample_certificate, boundary] 欄序回答。

固定的否是不從抽樣聲稱一般空間或未核點對的Hausdorff性；不否定前面的分離旗標。若實際已覆蓋全部有限點對，完整性仍須另行明示。

查看答案與解釋([[c5, a5, [[c5], [a5, b5]]]], 是, 1, 3, 否, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)

Wave6第五層核對=([[c5, a5, [[c5], [a5, b5]]]], 是, 1, 3, 否, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0081/)

Hausdorff空間 · qf-mod42-hausdorff-sampled-boundary · candidate





## 82. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-sampled-boundary；資料={"points":["a6","b6","c6"],"topology":[["a6","b6","c6"],["a6","b6"],["a6","c6"],["a6"],["c6"],[]],"sampled_pairs":[["c6","a6"]]}。請依 [sampled_pair_rows, all_sampled_separated, sample_count, total_pair_count, general_sample_certificate, boundary] 欄序回答。

固定的否是不從抽樣聲稱一般空間或未核點對的Hausdorff性；不否定前面的分離旗標。若實際已覆蓋全部有限點對，完整性仍須另行明示。

查看答案與解釋([[c6, a6, [[c6], [a6, b6]]]], 是, 1, 3, 否, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)

Wave6第五層核對=([[c6, a6, [[c6], [a6, b6]]]], 是, 1, 3, 否, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0082/)

Hausdorff空間 · qf-mod42-hausdorff-sampled-boundary · candidate





## 83. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-sampled-boundary；資料={"points":["a7","b7","c7"],"topology":[["a7","b7","c7"],["a7","b7"],["a7","c7"],["a7"],["c7"],[]],"sampled_pairs":[["c7","a7"]]}。請依 [sampled_pair_rows, all_sampled_separated, sample_count, total_pair_count, general_sample_certificate, boundary] 欄序回答。

固定的否是不從抽樣聲稱一般空間或未核點對的Hausdorff性；不否定前面的分離旗標。若實際已覆蓋全部有限點對，完整性仍須另行明示。

查看答案與解釋([[c7, a7, [[c7], [a7, b7]]]], 是, 1, 3, 否, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)

Wave6第五層核對=([[c7, a7, [[c7], [a7, b7]]]], 是, 1, 3, 否, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0083/)

Hausdorff空間 · qf-mod42-hausdorff-sampled-boundary · candidate





## 84. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-sampled-boundary；資料={"points":["a8","b8","c8"],"topology":[["a8","b8","c8"],["a8","b8"],["a8","c8"],["a8"],["c8"],[]],"sampled_pairs":[["c8","a8"]]}。請依 [sampled_pair_rows, all_sampled_separated, sample_count, total_pair_count, general_sample_certificate, boundary] 欄序回答。

固定的否是不從抽樣聲稱一般空間或未核點對的Hausdorff性；不否定前面的分離旗標。若實際已覆蓋全部有限點對，完整性仍須另行明示。

查看答案與解釋([[c8, a8, [[c8], [a8, b8]]]], 是, 1, 3, 否, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)

Wave6第五層核對=([[c8, a8, [[c8], [a8, b8]]]], 是, 1, 3, 否, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0084/)

Hausdorff空間 · qf-mod42-hausdorff-sampled-boundary · candidate





## 85. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-sampled-boundary；資料={"points":["a9","b9","c9"],"topology":[["a9","b9","c9"],["a9","b9"],["a9","c9"],["a9"],["c9"],[]],"sampled_pairs":[["c9","a9"]]}。請依 [sampled_pair_rows, all_sampled_separated, sample_count, total_pair_count, general_sample_certificate, boundary] 欄序回答。

固定的否是不從抽樣聲稱一般空間或未核點對的Hausdorff性；不否定前面的分離旗標。若實際已覆蓋全部有限點對，完整性仍須另行明示。

查看答案與解釋([[c9, a9, [[c9], [a9, b9]]]], 是, 1, 3, 否, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)

Wave6第五層核對=([[c9, a9, [[c9], [a9, b9]]]], 是, 1, 3, 否, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0085/)

Hausdorff空間 · qf-mod42-hausdorff-sampled-boundary · candidate





## 86. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-sampled-boundary；資料={"points":["a10","b10","c10"],"topology":[["a10","b10","c10"],["a10","b10"],["a10","c10"],["a10"],["c10"],[]],"sampled_pairs":[["c10","a10"]]}。請依 [sampled_pair_rows, all_sampled_separated, sample_count, total_pair_count, general_sample_certificate, boundary] 欄序回答。

固定的否是不從抽樣聲稱一般空間或未核點對的Hausdorff性；不否定前面的分離旗標。若實際已覆蓋全部有限點對，完整性仍須另行明示。

查看答案與解釋([[c10, a10, [[c10], [a10, b10]]]], 是, 1, 3, 否, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)

Wave6第五層核對=([[c10, a10, [[c10], [a10, b10]]]], 是, 1, 3, 否, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0086/)

Hausdorff空間 · qf-mod42-hausdorff-sampled-boundary · candidate





## 87. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-sampled-boundary；資料={"points":["a11","b11","c11"],"topology":[["a11","b11","c11"],["a11","b11"],["a11","c11"],["a11"],["c11"],[]],"sampled_pairs":[["c11","a11"]]}。請依 [sampled_pair_rows, all_sampled_separated, sample_count, total_pair_count, general_sample_certificate, boundary] 欄序回答。

固定的否是不從抽樣聲稱一般空間或未核點對的Hausdorff性；不否定前面的分離旗標。若實際已覆蓋全部有限點對，完整性仍須另行明示。

查看答案與解釋([[c11, a11, [[c11], [a11, b11]]]], 是, 1, 3, 否, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)

Wave6第五層核對=([[c11, a11, [[c11], [a11, b11]]]], 是, 1, 3, 否, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0087/)

Hausdorff空間 · qf-mod42-hausdorff-sampled-boundary · candidate





## 88. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-sampled-boundary；資料={"points":["a12","b12","c12"],"topology":[["a12","b12","c12"],["a12","b12"],["a12","c12"],["a12"],["c12"],[]],"sampled_pairs":[["c12","a12"]]}。請依 [sampled_pair_rows, all_sampled_separated, sample_count, total_pair_count, general_sample_certificate, boundary] 欄序回答。

固定的否是不從抽樣聲稱一般空間或未核點對的Hausdorff性；不否定前面的分離旗標。若實際已覆蓋全部有限點對，完整性仍須另行明示。

查看答案與解釋([[c12, a12, [[c12], [a12, b12]]]], 是, 1, 3, 否, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)

Wave6第五層核對=([[c12, a12, [[c12], [a12, b12]]]], 是, 1, 3, 否, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0088/)

Hausdorff空間 · qf-mod42-hausdorff-sampled-boundary · candidate





## 89. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-sampled-boundary；資料={"points":["a13","b13","c13"],"topology":[["a13","b13","c13"],["a13","b13"],["a13","c13"],["a13"],["c13"],[]],"sampled_pairs":[["c13","a13"]]}。請依 [sampled_pair_rows, all_sampled_separated, sample_count, total_pair_count, general_sample_certificate, boundary] 欄序回答。

固定的否是不從抽樣聲稱一般空間或未核點對的Hausdorff性；不否定前面的分離旗標。若實際已覆蓋全部有限點對，完整性仍須另行明示。

查看答案與解釋([[c13, a13, [[c13], [a13, b13]]]], 是, 1, 3, 否, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)

Wave6第五層核對=([[c13, a13, [[c13], [a13, b13]]]], 是, 1, 3, 否, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0089/)

Hausdorff空間 · qf-mod42-hausdorff-sampled-boundary · candidate





## 90. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-sampled-boundary；資料={"points":["a14","b14","c14"],"topology":[["a14","b14","c14"],["a14","b14"],["a14","c14"],["a14"],["c14"],[]],"sampled_pairs":[["c14","a14"]]}。請依 [sampled_pair_rows, all_sampled_separated, sample_count, total_pair_count, general_sample_certificate, boundary] 欄序回答。

固定的否是不從抽樣聲稱一般空間或未核點對的Hausdorff性；不否定前面的分離旗標。若實際已覆蓋全部有限點對，完整性仍須另行明示。

查看答案與解釋([[c14, a14, [[c14], [a14, b14]]]], 是, 1, 3, 否, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)

Wave6第五層核對=([[c14, a14, [[c14], [a14, b14]]]], 是, 1, 3, 否, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0090/)

Hausdorff空間 · qf-mod42-hausdorff-sampled-boundary · candidate





## 91. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-sampled-boundary；資料={"points":["a15","b15","c15"],"topology":[["a15","b15","c15"],["a15","b15"],["a15","c15"],["a15"],["c15"],[]],"sampled_pairs":[["c15","a15"]]}。請依 [sampled_pair_rows, all_sampled_separated, sample_count, total_pair_count, general_sample_certificate, boundary] 欄序回答。

固定的否是不從抽樣聲稱一般空間或未核點對的Hausdorff性；不否定前面的分離旗標。若實際已覆蓋全部有限點對，完整性仍須另行明示。

查看答案與解釋([[c15, a15, [[c15], [a15, b15]]]], 是, 1, 3, 否, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)

Wave6第五層核對=([[c15, a15, [[c15], [a15, b15]]]], 是, 1, 3, 否, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0091/)

Hausdorff空間 · qf-mod42-hausdorff-sampled-boundary · candidate





## 92. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-sampled-boundary；資料={"points":["a16","b16","c16"],"topology":[["a16","b16","c16"],["a16","b16"],["a16","c16"],["a16"],["c16"],[]],"sampled_pairs":[["c16","a16"]]}。請依 [sampled_pair_rows, all_sampled_separated, sample_count, total_pair_count, general_sample_certificate, boundary] 欄序回答。

固定的否是不從抽樣聲稱一般空間或未核點對的Hausdorff性；不否定前面的分離旗標。若實際已覆蓋全部有限點對，完整性仍須另行明示。

查看答案與解釋([[c16, a16, [[c16], [a16, b16]]]], 是, 1, 3, 否, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)

Wave6第五層核對=([[c16, a16, [[c16], [a16, b16]]]], 是, 1, 3, 否, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0092/)

Hausdorff空間 · qf-mod42-hausdorff-sampled-boundary · candidate





## 93. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-sampled-boundary；資料={"points":["a17","b17","c17"],"topology":[["a17","b17","c17"],["a17","b17"],["a17","c17"],["a17"],["c17"],[]],"sampled_pairs":[["c17","a17"]]}。請依 [sampled_pair_rows, all_sampled_separated, sample_count, total_pair_count, general_sample_certificate, boundary] 欄序回答。

固定的否是不從抽樣聲稱一般空間或未核點對的Hausdorff性；不否定前面的分離旗標。若實際已覆蓋全部有限點對，完整性仍須另行明示。

查看答案與解釋([[c17, a17, [[c17], [a17, b17]]]], 是, 1, 3, 否, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)

Wave6第五層核對=([[c17, a17, [[c17], [a17, b17]]]], 是, 1, 3, 否, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0093/)

Hausdorff空間 · qf-mod42-hausdorff-sampled-boundary · candidate





## 94. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-sampled-boundary；資料={"points":["a18","b18","c18"],"topology":[["a18","b18","c18"],["a18","b18"],["a18","c18"],["a18"],["c18"],[]],"sampled_pairs":[["c18","a18"]]}。請依 [sampled_pair_rows, all_sampled_separated, sample_count, total_pair_count, general_sample_certificate, boundary] 欄序回答。

固定的否是不從抽樣聲稱一般空間或未核點對的Hausdorff性；不否定前面的分離旗標。若實際已覆蓋全部有限點對，完整性仍須另行明示。

查看答案與解釋([[c18, a18, [[c18], [a18, b18]]]], 是, 1, 3, 否, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)

Wave6第五層核對=([[c18, a18, [[c18], [a18, b18]]]], 是, 1, 3, 否, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0094/)

Hausdorff空間 · qf-mod42-hausdorff-sampled-boundary · candidate





## 95. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-sampled-boundary；資料={"points":["a19","b19","c19"],"topology":[["a19","b19","c19"],["a19","b19"],["a19","c19"],["a19"],["c19"],[]],"sampled_pairs":[["c19","a19"]]}。請依 [sampled_pair_rows, all_sampled_separated, sample_count, total_pair_count, general_sample_certificate, boundary] 欄序回答。

固定的否是不從抽樣聲稱一般空間或未核點對的Hausdorff性；不否定前面的分離旗標。若實際已覆蓋全部有限點對，完整性仍須另行明示。

查看答案與解釋([[c19, a19, [[c19], [a19, b19]]]], 是, 1, 3, 否, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)

Wave6第五層核對=([[c19, a19, [[c19], [a19, b19]]]], 是, 1, 3, 否, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0095/)

Hausdorff空間 · qf-mod42-hausdorff-sampled-boundary · candidate





## 96. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-sampled-boundary；資料={"points":["a20","b20","c20"],"topology":[["a20","b20","c20"],["a20","b20"],["a20","c20"],["a20"],["c20"],[]],"sampled_pairs":[["c20","a20"]]}。請依 [sampled_pair_rows, all_sampled_separated, sample_count, total_pair_count, general_sample_certificate, boundary] 欄序回答。

固定的否是不從抽樣聲稱一般空間或未核點對的Hausdorff性；不否定前面的分離旗標。若實際已覆蓋全部有限點對，完整性仍須另行明示。

查看答案與解釋([[c20, a20, [[c20], [a20, b20]]]], 是, 1, 3, 否, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)

Wave6第五層核對=([[c20, a20, [[c20], [a20, b20]]]], 是, 1, 3, 否, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0096/)

Hausdorff空間 · qf-mod42-hausdorff-sampled-boundary · candidate





## 97. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-sampled-boundary；資料={"points":["a21","b21","c21"],"topology":[["a21","b21","c21"],["a21","b21"],["a21","c21"],["a21"],["c21"],[]],"sampled_pairs":[["c21","a21"]]}。請依 [sampled_pair_rows, all_sampled_separated, sample_count, total_pair_count, general_sample_certificate, boundary] 欄序回答。

固定的否是不從抽樣聲稱一般空間或未核點對的Hausdorff性；不否定前面的分離旗標。若實際已覆蓋全部有限點對，完整性仍須另行明示。

查看答案與解釋([[c21, a21, [[c21], [a21, b21]]]], 是, 1, 3, 否, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)

Wave6第五層核對=([[c21, a21, [[c21], [a21, b21]]]], 是, 1, 3, 否, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0097/)

Hausdorff空間 · qf-mod42-hausdorff-sampled-boundary · candidate





## 98. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-sampled-boundary；資料={"points":["a22","b22","c22"],"topology":[["a22","b22","c22"],["a22","b22"],["a22","c22"],["a22"],["c22"],[]],"sampled_pairs":[["c22","a22"]]}。請依 [sampled_pair_rows, all_sampled_separated, sample_count, total_pair_count, general_sample_certificate, boundary] 欄序回答。

固定的否是不從抽樣聲稱一般空間或未核點對的Hausdorff性；不否定前面的分離旗標。若實際已覆蓋全部有限點對，完整性仍須另行明示。

查看答案與解釋([[c22, a22, [[c22], [a22, b22]]]], 是, 1, 3, 否, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)

Wave6第五層核對=([[c22, a22, [[c22], [a22, b22]]]], 是, 1, 3, 否, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0098/)

Hausdorff空間 · qf-mod42-hausdorff-sampled-boundary · candidate





## 99. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-sampled-boundary；資料={"points":["a23","b23","c23"],"topology":[["a23","b23","c23"],["a23","b23"],["a23","c23"],["a23"],["c23"],[]],"sampled_pairs":[["c23","a23"]]}。請依 [sampled_pair_rows, all_sampled_separated, sample_count, total_pair_count, general_sample_certificate, boundary] 欄序回答。

固定的否是不從抽樣聲稱一般空間或未核點對的Hausdorff性；不否定前面的分離旗標。若實際已覆蓋全部有限點對，完整性仍須另行明示。

查看答案與解釋([[c23, a23, [[c23], [a23, b23]]]], 是, 1, 3, 否, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)

Wave6第五層核對=([[c23, a23, [[c23], [a23, b23]]]], 是, 1, 3, 否, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0099/)

Hausdorff空間 · qf-mod42-hausdorff-sampled-boundary · candidate





## 100. Hausdorff空間

完整有限拓撲上每一對distinct points的disjoint open-neighborhood witnesses。操作=hausdorff-sampled-boundary；資料={"points":["a24","b24","c24"],"topology":[["a24","b24","c24"],["a24","b24"],["a24","c24"],["a24"],["c24"],[]],"sampled_pairs":[["c24","a24"]]}。請依 [sampled_pair_rows, all_sampled_separated, sample_count, total_pair_count, general_sample_certificate, boundary] 欄序回答。

固定的否是不從抽樣聲稱一般空間或未核點對的Hausdorff性；不否定前面的分離旗標。若實際已覆蓋全部有限點對，完整性仍須另行明示。

查看答案與解釋([[c24, a24, [[c24], [a24, b24]]]], 是, 1, 3, 否, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)

Wave6第五層核對=([[c24, a24, [[c24], [a24, b24]]]], 是, 1, 3, 否, successful_sampled_pairs_do_not_certify_unchecked_pairs_or_infinite_spaces)；依完整明示資料獨立重算；一個失敗pair即可證non-Hausdorff；empty與singleton vacuously Hausdorff；sampled成功pairs不足以證unchecked或infinite spaces；finite Hausdorff implies discrete不可外推。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r03-hausdorff-space-0100/)

Hausdorff空間 · qf-mod42-hausdorff-sampled-boundary · candidate



[原始題目 JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261014-advance-20261111-r03-hausdorff-space-foundations/questions.jsonl) · [驗收報告](https://ocme.evemisslab.com/data/questions/batches/batch-20261014-advance-20261111-r03-hausdorff-space-foundations/validation-report.json)