# OCME ยท Knowledge & practice explorer 302 MKO / 1,441 families / 360 batches / 36,000 questions. 36,000 second-context math/bilingual reviewed; 0 display/symbol-checked candidates. Source questions: candidate. English: ai_candidate. No new proof, Lean, SREG or training. 100 results; page 3/4. ## Question 22951: A Pair Separator Must Use Two Actual Disjoint Open Neighborhoods - ID: `q-20261014-advance-20261111-r03-hausdorff-space-0001`; number: 22951 - Processing: second_context_reviewed - MKO: [mko-hausdorff-space](/en/mko/mko-hausdorff-space/) - Family: [qf-mod42-hausdorff-pair-separator](/en/explore/?family=qf-mod42-hausdorff-pair-separator) - Batch: [batch-20261014-advance-20261111-r03-hausdorff-space-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r03-hausdorff-space-foundations) - [Derivation](/en/questions/q-20261014-advance-20261111-r03-hausdorff-space-0001/) / [Markdown](/en/questions/q-20261014-advance-20261111-r03-hausdorff-space-0001/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r03-hausdorff-space-0001.json) ## Question 22952: A Pair Separator Must Use Two Actual Disjoint Open Neighborhoods - ID: `q-20261014-advance-20261111-r03-hausdorff-space-0002`; number: 22952 - Processing: second_context_reviewed - MKO: [mko-hausdorff-space](/en/mko/mko-hausdorff-space/) - Family: [qf-mod42-hausdorff-pair-separator](/en/explore/?family=qf-mod42-hausdorff-pair-separator) - Batch: [batch-20261014-advance-20261111-r03-hausdorff-space-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r03-hausdorff-space-foundations) - [Derivation](/en/questions/q-20261014-advance-20261111-r03-hausdorff-space-0002/) / [Markdown](/en/questions/q-20261014-advance-20261111-r03-hausdorff-space-0002/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r03-hausdorff-space-0002.json) ## Question 22953: A Pair Separator Must Use Two Actual Disjoint Open Neighborhoods - ID: `q-20261014-advance-20261111-r03-hausdorff-space-0003`; number: 22953 - Processing: second_context_reviewed - MKO: [mko-hausdorff-space](/en/mko/mko-hausdorff-space/) - Family: [qf-mod42-hausdorff-pair-separator](/en/explore/?family=qf-mod42-hausdorff-pair-separator) - Batch: [batch-20261014-advance-20261111-r03-hausdorff-space-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r03-hausdorff-space-foundations) - [Derivation](/en/questions/q-20261014-advance-20261111-r03-hausdorff-space-0003/) / [Markdown](/en/questions/q-20261014-advance-20261111-r03-hausdorff-space-0003/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r03-hausdorff-space-0003.json) ## Question 22954: A Pair Separator Must Use Two Actual Disjoint Open Neighborhoods - ID: `q-20261014-advance-20261111-r03-hausdorff-space-0004`; number: 22954 - Processing: second_context_reviewed - MKO: [mko-hausdorff-space](/en/mko/mko-hausdorff-space/) - Family: [qf-mod42-hausdorff-pair-separator](/en/explore/?family=qf-mod42-hausdorff-pair-separator) - Batch: [batch-20261014-advance-20261111-r03-hausdorff-space-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r03-hausdorff-space-foundations) - [Derivation](/en/questions/q-20261014-advance-20261111-r03-hausdorff-space-0004/) / [Markdown](/en/questions/q-20261014-advance-20261111-r03-hausdorff-space-0004/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r03-hausdorff-space-0004.json) ## Question 22955: A Pair Separator Must Use Two Actual Disjoint Open Neighborhoods - ID: `q-20261014-advance-20261111-r03-hausdorff-space-0005`; number: 22955 - Processing: second_context_reviewed - MKO: [mko-hausdorff-space](/en/mko/mko-hausdorff-space/) - Family: [qf-mod42-hausdorff-pair-separator](/en/explore/?family=qf-mod42-hausdorff-pair-separator) - Batch: [batch-20261014-advance-20261111-r03-hausdorff-space-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r03-hausdorff-space-foundations) - [Derivation](/en/questions/q-20261014-advance-20261111-r03-hausdorff-space-0005/) / [Markdown](/en/questions/q-20261014-advance-20261111-r03-hausdorff-space-0005/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r03-hausdorff-space-0005.json) ## Question 22956: A Pair Separator Must Use Two Actual Disjoint Open Neighborhoods - ID: `q-20261014-advance-20261111-r03-hausdorff-space-0006`; number: 22956 - Processing: second_context_reviewed - MKO: [mko-hausdorff-space](/en/mko/mko-hausdorff-space/) - Family: [qf-mod42-hausdorff-pair-separator](/en/explore/?family=qf-mod42-hausdorff-pair-separator) - Batch: [batch-20261014-advance-20261111-r03-hausdorff-space-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r03-hausdorff-space-foundations) - [Derivation](/en/questions/q-20261014-advance-20261111-r03-hausdorff-space-0006/) / [Markdown](/en/questions/q-20261014-advance-20261111-r03-hausdorff-space-0006/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r03-hausdorff-space-0006.json) ## Question 22957: A Pair Separator Must Use Two Actual Disjoint Open Neighborhoods - ID: `q-20261014-advance-20261111-r03-hausdorff-space-0007`; number: 22957 - Processing: second_context_reviewed - MKO: [mko-hausdorff-space](/en/mko/mko-hausdorff-space/) - Family: [qf-mod42-hausdorff-pair-separator](/en/explore/?family=qf-mod42-hausdorff-pair-separator) - Batch: [batch-20261014-advance-20261111-r03-hausdorff-space-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r03-hausdorff-space-foundations) - [Derivation](/en/questions/q-20261014-advance-20261111-r03-hausdorff-space-0007/) / [Markdown](/en/questions/q-20261014-advance-20261111-r03-hausdorff-space-0007/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r03-hausdorff-space-0007.json) ## Question 22958: A Pair Separator Must Use Two Actual Disjoint Open Neighborhoods - ID: `q-20261014-advance-20261111-r03-hausdorff-space-0008`; number: 22958 - Processing: second_context_reviewed - MKO: [mko-hausdorff-space](/en/mko/mko-hausdorff-space/) - Family: [qf-mod42-hausdorff-pair-separator](/en/explore/?family=qf-mod42-hausdorff-pair-separator) - Batch: [batch-20261014-advance-20261111-r03-hausdorff-space-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r03-hausdorff-space-foundations) - [Derivation](/en/questions/q-20261014-advance-20261111-r03-hausdorff-space-0008/) / [Markdown](/en/questions/q-20261014-advance-20261111-r03-hausdorff-space-0008/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r03-hausdorff-space-0008.json) ## Question 22959: A Pair Separator Must Use Two Actual Disjoint Open Neighborhoods - ID: `q-20261014-advance-20261111-r03-hausdorff-space-0009`; number: 22959 - Processing: second_context_reviewed - MKO: [mko-hausdorff-space](/en/mko/mko-hausdorff-space/) - Family: [qf-mod42-hausdorff-pair-separator](/en/explore/?family=qf-mod42-hausdorff-pair-separator) - Batch: [batch-20261014-advance-20261111-r03-hausdorff-space-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r03-hausdorff-space-foundations) - [Derivation](/en/questions/q-20261014-advance-20261111-r03-hausdorff-space-0009/) / [Markdown](/en/questions/q-20261014-advance-20261111-r03-hausdorff-space-0009/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r03-hausdorff-space-0009.json) ## Question 22960: A Pair Separator Must Use Two Actual Disjoint Open Neighborhoods - ID: `q-20261014-advance-20261111-r03-hausdorff-space-0010`; number: 22960 - Processing: second_context_reviewed - MKO: [mko-hausdorff-space](/en/mko/mko-hausdorff-space/) - Family: [qf-mod42-hausdorff-pair-separator](/en/explore/?family=qf-mod42-hausdorff-pair-separator) - Batch: [batch-20261014-advance-20261111-r03-hausdorff-space-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r03-hausdorff-space-foundations) - [Derivation](/en/questions/q-20261014-advance-20261111-r03-hausdorff-space-0010/) / [Markdown](/en/questions/q-20261014-advance-20261111-r03-hausdorff-space-0010/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r03-hausdorff-space-0010.json) ## Question 22961: A Pair Separator Must Use Two Actual Disjoint Open Neighborhoods - ID: `q-20261014-advance-20261111-r03-hausdorff-space-0011`; number: 22961 - Processing: second_context_reviewed - MKO: [mko-hausdorff-space](/en/mko/mko-hausdorff-space/) - Family: [qf-mod42-hausdorff-pair-separator](/en/explore/?family=qf-mod42-hausdorff-pair-separator) - Batch: [batch-20261014-advance-20261111-r03-hausdorff-space-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r03-hausdorff-space-foundations) - [Derivation](/en/questions/q-20261014-advance-20261111-r03-hausdorff-space-0011/) / [Markdown](/en/questions/q-20261014-advance-20261111-r03-hausdorff-space-0011/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r03-hausdorff-space-0011.json) ## Question 22962: A Pair Separator Must Use Two Actual Disjoint Open Neighborhoods - ID: `q-20261014-advance-20261111-r03-hausdorff-space-0012`; number: 22962 - Processing: second_context_reviewed - MKO: [mko-hausdorff-space](/en/mko/mko-hausdorff-space/) - Family: [qf-mod42-hausdorff-pair-separator](/en/explore/?family=qf-mod42-hausdorff-pair-separator) - Batch: [batch-20261014-advance-20261111-r03-hausdorff-space-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r03-hausdorff-space-foundations) - [Derivation](/en/questions/q-20261014-advance-20261111-r03-hausdorff-space-0012/) / [Markdown](/en/questions/q-20261014-advance-20261111-r03-hausdorff-space-0012/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r03-hausdorff-space-0012.json) ## Question 22963: A Pair Separator Must Use Two Actual Disjoint Open Neighborhoods - ID: `q-20261014-advance-20261111-r03-hausdorff-space-0013`; number: 22963 - Processing: second_context_reviewed - MKO: [mko-hausdorff-space](/en/mko/mko-hausdorff-space/) - Family: [qf-mod42-hausdorff-pair-separator](/en/explore/?family=qf-mod42-hausdorff-pair-separator) - Batch: [batch-20261014-advance-20261111-r03-hausdorff-space-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r03-hausdorff-space-foundations) - [Derivation](/en/questions/q-20261014-advance-20261111-r03-hausdorff-space-0013/) / [Markdown](/en/questions/q-20261014-advance-20261111-r03-hausdorff-space-0013/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r03-hausdorff-space-0013.json) ## Question 22964: A Pair Separator Must Use Two Actual Disjoint Open Neighborhoods - ID: `q-20261014-advance-20261111-r03-hausdorff-space-0014`; number: 22964 - Processing: second_context_reviewed - MKO: [mko-hausdorff-space](/en/mko/mko-hausdorff-space/) - Family: [qf-mod42-hausdorff-pair-separator](/en/explore/?family=qf-mod42-hausdorff-pair-separator) - Batch: [batch-20261014-advance-20261111-r03-hausdorff-space-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r03-hausdorff-space-foundations) - [Derivation](/en/questions/q-20261014-advance-20261111-r03-hausdorff-space-0014/) / [Markdown](/en/questions/q-20261014-advance-20261111-r03-hausdorff-space-0014/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r03-hausdorff-space-0014.json) ## Question 22965: A Pair Separator Must Use Two Actual Disjoint Open Neighborhoods - ID: `q-20261014-advance-20261111-r03-hausdorff-space-0015`; number: 22965 - Processing: second_context_reviewed - MKO: [mko-hausdorff-space](/en/mko/mko-hausdorff-space/) - Family: [qf-mod42-hausdorff-pair-separator](/en/explore/?family=qf-mod42-hausdorff-pair-separator) - Batch: [batch-20261014-advance-20261111-r03-hausdorff-space-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r03-hausdorff-space-foundations) - [Derivation](/en/questions/q-20261014-advance-20261111-r03-hausdorff-space-0015/) / [Markdown](/en/questions/q-20261014-advance-20261111-r03-hausdorff-space-0015/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r03-hausdorff-space-0015.json) ## Question 22966: A Pair Separator Must Use Two Actual Disjoint Open Neighborhoods - ID: `q-20261014-advance-20261111-r03-hausdorff-space-0016`; number: 22966 - Processing: second_context_reviewed - MKO: [mko-hausdorff-space](/en/mko/mko-hausdorff-space/) - Family: [qf-mod42-hausdorff-pair-separator](/en/explore/?family=qf-mod42-hausdorff-pair-separator) - Batch: [batch-20261014-advance-20261111-r03-hausdorff-space-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r03-hausdorff-space-foundations) - [Derivation](/en/questions/q-20261014-advance-20261111-r03-hausdorff-space-0016/) / [Markdown](/en/questions/q-20261014-advance-20261111-r03-hausdorff-space-0016/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r03-hausdorff-space-0016.json) ## Question 22967: A Pair Separator Must Use Two Actual Disjoint Open Neighborhoods - ID: `q-20261014-advance-20261111-r03-hausdorff-space-0017`; number: 22967 - Processing: second_context_reviewed - MKO: [mko-hausdorff-space](/en/mko/mko-hausdorff-space/) - Family: [qf-mod42-hausdorff-pair-separator](/en/explore/?family=qf-mod42-hausdorff-pair-separator) - Batch: [batch-20261014-advance-20261111-r03-hausdorff-space-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r03-hausdorff-space-foundations) - [Derivation](/en/questions/q-20261014-advance-20261111-r03-hausdorff-space-0017/) / [Markdown](/en/questions/q-20261014-advance-20261111-r03-hausdorff-space-0017/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r03-hausdorff-space-0017.json) ## Question 22968: A Pair Separator Must Use Two Actual Disjoint Open Neighborhoods - ID: `q-20261014-advance-20261111-r03-hausdorff-space-0018`; number: 22968 - Processing: second_context_reviewed - MKO: [mko-hausdorff-space](/en/mko/mko-hausdorff-space/) - Family: [qf-mod42-hausdorff-pair-separator](/en/explore/?family=qf-mod42-hausdorff-pair-separator) - Batch: [batch-20261014-advance-20261111-r03-hausdorff-space-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r03-hausdorff-space-foundations) - [Derivation](/en/questions/q-20261014-advance-20261111-r03-hausdorff-space-0018/) / [Markdown](/en/questions/q-20261014-advance-20261111-r03-hausdorff-space-0018/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r03-hausdorff-space-0018.json) ## Question 22969: A Pair Separator Must Use Two Actual Disjoint Open Neighborhoods - ID: `q-20261014-advance-20261111-r03-hausdorff-space-0019`; number: 22969 - Processing: second_context_reviewed - MKO: [mko-hausdorff-space](/en/mko/mko-hausdorff-space/) - Family: [qf-mod42-hausdorff-pair-separator](/en/explore/?family=qf-mod42-hausdorff-pair-separator) - Batch: [batch-20261014-advance-20261111-r03-hausdorff-space-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r03-hausdorff-space-foundations) - [Derivation](/en/questions/q-20261014-advance-20261111-r03-hausdorff-space-0019/) / [Markdown](/en/questions/q-20261014-advance-20261111-r03-hausdorff-space-0019/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r03-hausdorff-space-0019.json) ## Question 22970: A Pair Separator Must Use Two Actual Disjoint Open Neighborhoods - ID: `q-20261014-advance-20261111-r03-hausdorff-space-0020`; number: 22970 - Processing: second_context_reviewed - MKO: [mko-hausdorff-space](/en/mko/mko-hausdorff-space/) - Family: [qf-mod42-hausdorff-pair-separator](/en/explore/?family=qf-mod42-hausdorff-pair-separator) - Batch: [batch-20261014-advance-20261111-r03-hausdorff-space-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r03-hausdorff-space-foundations) - [Derivation](/en/questions/q-20261014-advance-20261111-r03-hausdorff-space-0020/) / [Markdown](/en/questions/q-20261014-advance-20261111-r03-hausdorff-space-0020/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r03-hausdorff-space-0020.json) ## Question 22971: A Pair Separator Must Use Two Actual Disjoint Open Neighborhoods - ID: `q-20261014-advance-20261111-r03-hausdorff-space-0021`; number: 22971 - Processing: second_context_reviewed - MKO: [mko-hausdorff-space](/en/mko/mko-hausdorff-space/) - Family: [qf-mod42-hausdorff-pair-separator](/en/explore/?family=qf-mod42-hausdorff-pair-separator) - Batch: [batch-20261014-advance-20261111-r03-hausdorff-space-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r03-hausdorff-space-foundations) - [Derivation](/en/questions/q-20261014-advance-20261111-r03-hausdorff-space-0021/) / [Markdown](/en/questions/q-20261014-advance-20261111-r03-hausdorff-space-0021/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r03-hausdorff-space-0021.json) ## Question 22972: A Pair Separator Must Use Two Actual Disjoint Open Neighborhoods - ID: `q-20261014-advance-20261111-r03-hausdorff-space-0022`; number: 22972 - Processing: second_context_reviewed - MKO: [mko-hausdorff-space](/en/mko/mko-hausdorff-space/) - Family: [qf-mod42-hausdorff-pair-separator](/en/explore/?family=qf-mod42-hausdorff-pair-separator) - Batch: [batch-20261014-advance-20261111-r03-hausdorff-space-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r03-hausdorff-space-foundations) - [Derivation](/en/questions/q-20261014-advance-20261111-r03-hausdorff-space-0022/) / [Markdown](/en/questions/q-20261014-advance-20261111-r03-hausdorff-space-0022/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r03-hausdorff-space-0022.json) ## Question 22973: A Pair Separator Must Use Two Actual Disjoint Open Neighborhoods - ID: `q-20261014-advance-20261111-r03-hausdorff-space-0023`; number: 22973 - Processing: second_context_reviewed - MKO: [mko-hausdorff-space](/en/mko/mko-hausdorff-space/) - Family: [qf-mod42-hausdorff-pair-separator](/en/explore/?family=qf-mod42-hausdorff-pair-separator) - Batch: [batch-20261014-advance-20261111-r03-hausdorff-space-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r03-hausdorff-space-foundations) - [Derivation](/en/questions/q-20261014-advance-20261111-r03-hausdorff-space-0023/) / [Markdown](/en/questions/q-20261014-advance-20261111-r03-hausdorff-space-0023/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r03-hausdorff-space-0023.json) ## Question 22974: A Pair Separator Must Use Two Actual Disjoint Open Neighborhoods - ID: `q-20261014-advance-20261111-r03-hausdorff-space-0024`; number: 22974 - Processing: second_context_reviewed - MKO: [mko-hausdorff-space](/en/mko/mko-hausdorff-space/) - Family: [qf-mod42-hausdorff-pair-separator](/en/explore/?family=qf-mod42-hausdorff-pair-separator) - Batch: [batch-20261014-advance-20261111-r03-hausdorff-space-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r03-hausdorff-space-foundations) - [Derivation](/en/questions/q-20261014-advance-20261111-r03-hausdorff-space-0024/) / [Markdown](/en/questions/q-20261014-advance-20261111-r03-hausdorff-space-0024/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r03-hausdorff-space-0024.json) ## Question 22975: A Pair Separator Must Use Two Actual Disjoint Open Neighborhoods - ID: `q-20261014-advance-20261111-r03-hausdorff-space-0025`; number: 22975 - Processing: second_context_reviewed - MKO: [mko-hausdorff-space](/en/mko/mko-hausdorff-space/) - Family: [qf-mod42-hausdorff-pair-separator](/en/explore/?family=qf-mod42-hausdorff-pair-separator) - Batch: [batch-20261014-advance-20261111-r03-hausdorff-space-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r03-hausdorff-space-foundations) - [Derivation](/en/questions/q-20261014-advance-20261111-r03-hausdorff-space-0025/) / [Markdown](/en/questions/q-20261014-advance-20261111-r03-hausdorff-space-0025/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r03-hausdorff-space-0025.json) [Next](/en/explore/index.md?mko=mko-hausdorff-space&page=4)