# 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. 25 results; page 1/1. ## Question 17301: A Clopen Witness Must Also Be Nontrivial - ID: `q-20261014-advance-20261103-r05-connected-topological-space-0026`; number: 17301 - Processing: second_context_reviewed - MKO: [mko-connected-topological-space](/en/mko/mko-connected-topological-space/) - Family: [qf-mod34-connected-clopen-witness](/en/explore/?family=qf-mod34-connected-clopen-witness) - Batch: [batch-20261014-advance-20261103-r05-connected-topological-space-foundations](/en/explore/?batch=batch-20261014-advance-20261103-r05-connected-topological-space-foundations) - [Derivation](/en/questions/q-20261014-advance-20261103-r05-connected-topological-space-0026/) / [Markdown](/en/questions/q-20261014-advance-20261103-r05-connected-topological-space-0026/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261103-r05-connected-topological-space-0026.json) ## Question 17302: A Clopen Witness Must Also Be Nontrivial - ID: `q-20261014-advance-20261103-r05-connected-topological-space-0027`; number: 17302 - Processing: second_context_reviewed - MKO: [mko-connected-topological-space](/en/mko/mko-connected-topological-space/) - Family: [qf-mod34-connected-clopen-witness](/en/explore/?family=qf-mod34-connected-clopen-witness) - Batch: [batch-20261014-advance-20261103-r05-connected-topological-space-foundations](/en/explore/?batch=batch-20261014-advance-20261103-r05-connected-topological-space-foundations) - [Derivation](/en/questions/q-20261014-advance-20261103-r05-connected-topological-space-0027/) / [Markdown](/en/questions/q-20261014-advance-20261103-r05-connected-topological-space-0027/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261103-r05-connected-topological-space-0027.json) ## Question 17303: A Clopen Witness Must Also Be Nontrivial - ID: `q-20261014-advance-20261103-r05-connected-topological-space-0028`; number: 17303 - Processing: second_context_reviewed - MKO: [mko-connected-topological-space](/en/mko/mko-connected-topological-space/) - Family: [qf-mod34-connected-clopen-witness](/en/explore/?family=qf-mod34-connected-clopen-witness) - Batch: [batch-20261014-advance-20261103-r05-connected-topological-space-foundations](/en/explore/?batch=batch-20261014-advance-20261103-r05-connected-topological-space-foundations) - [Derivation](/en/questions/q-20261014-advance-20261103-r05-connected-topological-space-0028/) / [Markdown](/en/questions/q-20261014-advance-20261103-r05-connected-topological-space-0028/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261103-r05-connected-topological-space-0028.json) ## Question 17304: A Clopen Witness Must Also Be Nontrivial - ID: `q-20261014-advance-20261103-r05-connected-topological-space-0029`; number: 17304 - Processing: second_context_reviewed - MKO: [mko-connected-topological-space](/en/mko/mko-connected-topological-space/) - Family: [qf-mod34-connected-clopen-witness](/en/explore/?family=qf-mod34-connected-clopen-witness) - Batch: [batch-20261014-advance-20261103-r05-connected-topological-space-foundations](/en/explore/?batch=batch-20261014-advance-20261103-r05-connected-topological-space-foundations) - [Derivation](/en/questions/q-20261014-advance-20261103-r05-connected-topological-space-0029/) / [Markdown](/en/questions/q-20261014-advance-20261103-r05-connected-topological-space-0029/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261103-r05-connected-topological-space-0029.json) ## Question 17305: A Clopen Witness Must Also Be Nontrivial - ID: `q-20261014-advance-20261103-r05-connected-topological-space-0030`; number: 17305 - Processing: second_context_reviewed - MKO: [mko-connected-topological-space](/en/mko/mko-connected-topological-space/) - Family: [qf-mod34-connected-clopen-witness](/en/explore/?family=qf-mod34-connected-clopen-witness) - Batch: [batch-20261014-advance-20261103-r05-connected-topological-space-foundations](/en/explore/?batch=batch-20261014-advance-20261103-r05-connected-topological-space-foundations) - [Derivation](/en/questions/q-20261014-advance-20261103-r05-connected-topological-space-0030/) / [Markdown](/en/questions/q-20261014-advance-20261103-r05-connected-topological-space-0030/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261103-r05-connected-topological-space-0030.json) ## Question 17306: A Clopen Witness Must Also Be Nontrivial - ID: `q-20261014-advance-20261103-r05-connected-topological-space-0031`; number: 17306 - Processing: second_context_reviewed - MKO: [mko-connected-topological-space](/en/mko/mko-connected-topological-space/) - Family: [qf-mod34-connected-clopen-witness](/en/explore/?family=qf-mod34-connected-clopen-witness) - Batch: [batch-20261014-advance-20261103-r05-connected-topological-space-foundations](/en/explore/?batch=batch-20261014-advance-20261103-r05-connected-topological-space-foundations) - [Derivation](/en/questions/q-20261014-advance-20261103-r05-connected-topological-space-0031/) / [Markdown](/en/questions/q-20261014-advance-20261103-r05-connected-topological-space-0031/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261103-r05-connected-topological-space-0031.json) ## Question 17307: A Clopen Witness Must Also Be Nontrivial - ID: `q-20261014-advance-20261103-r05-connected-topological-space-0032`; number: 17307 - Processing: second_context_reviewed - MKO: [mko-connected-topological-space](/en/mko/mko-connected-topological-space/) - Family: [qf-mod34-connected-clopen-witness](/en/explore/?family=qf-mod34-connected-clopen-witness) - Batch: [batch-20261014-advance-20261103-r05-connected-topological-space-foundations](/en/explore/?batch=batch-20261014-advance-20261103-r05-connected-topological-space-foundations) - [Derivation](/en/questions/q-20261014-advance-20261103-r05-connected-topological-space-0032/) / [Markdown](/en/questions/q-20261014-advance-20261103-r05-connected-topological-space-0032/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261103-r05-connected-topological-space-0032.json) ## Question 17308: A Clopen Witness Must Also Be Nontrivial - ID: `q-20261014-advance-20261103-r05-connected-topological-space-0033`; number: 17308 - Processing: second_context_reviewed - MKO: [mko-connected-topological-space](/en/mko/mko-connected-topological-space/) - Family: [qf-mod34-connected-clopen-witness](/en/explore/?family=qf-mod34-connected-clopen-witness) - Batch: [batch-20261014-advance-20261103-r05-connected-topological-space-foundations](/en/explore/?batch=batch-20261014-advance-20261103-r05-connected-topological-space-foundations) - [Derivation](/en/questions/q-20261014-advance-20261103-r05-connected-topological-space-0033/) / [Markdown](/en/questions/q-20261014-advance-20261103-r05-connected-topological-space-0033/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261103-r05-connected-topological-space-0033.json) ## Question 17309: A Clopen Witness Must Also Be Nontrivial - ID: `q-20261014-advance-20261103-r05-connected-topological-space-0034`; number: 17309 - Processing: second_context_reviewed - MKO: [mko-connected-topological-space](/en/mko/mko-connected-topological-space/) - Family: [qf-mod34-connected-clopen-witness](/en/explore/?family=qf-mod34-connected-clopen-witness) - Batch: [batch-20261014-advance-20261103-r05-connected-topological-space-foundations](/en/explore/?batch=batch-20261014-advance-20261103-r05-connected-topological-space-foundations) - [Derivation](/en/questions/q-20261014-advance-20261103-r05-connected-topological-space-0034/) / [Markdown](/en/questions/q-20261014-advance-20261103-r05-connected-topological-space-0034/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261103-r05-connected-topological-space-0034.json) ## Question 17310: A Clopen Witness Must Also Be Nontrivial - ID: `q-20261014-advance-20261103-r05-connected-topological-space-0035`; number: 17310 - Processing: second_context_reviewed - MKO: [mko-connected-topological-space](/en/mko/mko-connected-topological-space/) - Family: [qf-mod34-connected-clopen-witness](/en/explore/?family=qf-mod34-connected-clopen-witness) - Batch: [batch-20261014-advance-20261103-r05-connected-topological-space-foundations](/en/explore/?batch=batch-20261014-advance-20261103-r05-connected-topological-space-foundations) - [Derivation](/en/questions/q-20261014-advance-20261103-r05-connected-topological-space-0035/) / [Markdown](/en/questions/q-20261014-advance-20261103-r05-connected-topological-space-0035/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261103-r05-connected-topological-space-0035.json) ## Question 17311: A Clopen Witness Must Also Be Nontrivial - ID: `q-20261014-advance-20261103-r05-connected-topological-space-0036`; number: 17311 - Processing: second_context_reviewed - MKO: [mko-connected-topological-space](/en/mko/mko-connected-topological-space/) - Family: [qf-mod34-connected-clopen-witness](/en/explore/?family=qf-mod34-connected-clopen-witness) - Batch: [batch-20261014-advance-20261103-r05-connected-topological-space-foundations](/en/explore/?batch=batch-20261014-advance-20261103-r05-connected-topological-space-foundations) - [Derivation](/en/questions/q-20261014-advance-20261103-r05-connected-topological-space-0036/) / [Markdown](/en/questions/q-20261014-advance-20261103-r05-connected-topological-space-0036/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261103-r05-connected-topological-space-0036.json) ## Question 17312: A Clopen Witness Must Also Be Nontrivial - ID: `q-20261014-advance-20261103-r05-connected-topological-space-0037`; number: 17312 - Processing: second_context_reviewed - MKO: [mko-connected-topological-space](/en/mko/mko-connected-topological-space/) - Family: [qf-mod34-connected-clopen-witness](/en/explore/?family=qf-mod34-connected-clopen-witness) - Batch: [batch-20261014-advance-20261103-r05-connected-topological-space-foundations](/en/explore/?batch=batch-20261014-advance-20261103-r05-connected-topological-space-foundations) - [Derivation](/en/questions/q-20261014-advance-20261103-r05-connected-topological-space-0037/) / [Markdown](/en/questions/q-20261014-advance-20261103-r05-connected-topological-space-0037/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261103-r05-connected-topological-space-0037.json) ## Question 17313: A Clopen Witness Must Also Be Nontrivial - ID: `q-20261014-advance-20261103-r05-connected-topological-space-0038`; number: 17313 - Processing: second_context_reviewed - MKO: [mko-connected-topological-space](/en/mko/mko-connected-topological-space/) - Family: [qf-mod34-connected-clopen-witness](/en/explore/?family=qf-mod34-connected-clopen-witness) - Batch: [batch-20261014-advance-20261103-r05-connected-topological-space-foundations](/en/explore/?batch=batch-20261014-advance-20261103-r05-connected-topological-space-foundations) - [Derivation](/en/questions/q-20261014-advance-20261103-r05-connected-topological-space-0038/) / [Markdown](/en/questions/q-20261014-advance-20261103-r05-connected-topological-space-0038/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261103-r05-connected-topological-space-0038.json) ## Question 17314: A Clopen Witness Must Also Be Nontrivial - ID: `q-20261014-advance-20261103-r05-connected-topological-space-0039`; number: 17314 - Processing: second_context_reviewed - MKO: [mko-connected-topological-space](/en/mko/mko-connected-topological-space/) - Family: [qf-mod34-connected-clopen-witness](/en/explore/?family=qf-mod34-connected-clopen-witness) - Batch: [batch-20261014-advance-20261103-r05-connected-topological-space-foundations](/en/explore/?batch=batch-20261014-advance-20261103-r05-connected-topological-space-foundations) - [Derivation](/en/questions/q-20261014-advance-20261103-r05-connected-topological-space-0039/) / [Markdown](/en/questions/q-20261014-advance-20261103-r05-connected-topological-space-0039/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261103-r05-connected-topological-space-0039.json) ## Question 17315: A Clopen Witness Must Also Be Nontrivial - ID: `q-20261014-advance-20261103-r05-connected-topological-space-0040`; number: 17315 - Processing: second_context_reviewed - MKO: [mko-connected-topological-space](/en/mko/mko-connected-topological-space/) - Family: [qf-mod34-connected-clopen-witness](/en/explore/?family=qf-mod34-connected-clopen-witness) - Batch: [batch-20261014-advance-20261103-r05-connected-topological-space-foundations](/en/explore/?batch=batch-20261014-advance-20261103-r05-connected-topological-space-foundations) - [Derivation](/en/questions/q-20261014-advance-20261103-r05-connected-topological-space-0040/) / [Markdown](/en/questions/q-20261014-advance-20261103-r05-connected-topological-space-0040/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261103-r05-connected-topological-space-0040.json) ## Question 17316: A Clopen Witness Must Also Be Nontrivial - ID: `q-20261014-advance-20261103-r05-connected-topological-space-0041`; number: 17316 - Processing: second_context_reviewed - MKO: [mko-connected-topological-space](/en/mko/mko-connected-topological-space/) - Family: [qf-mod34-connected-clopen-witness](/en/explore/?family=qf-mod34-connected-clopen-witness) - Batch: [batch-20261014-advance-20261103-r05-connected-topological-space-foundations](/en/explore/?batch=batch-20261014-advance-20261103-r05-connected-topological-space-foundations) - [Derivation](/en/questions/q-20261014-advance-20261103-r05-connected-topological-space-0041/) / [Markdown](/en/questions/q-20261014-advance-20261103-r05-connected-topological-space-0041/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261103-r05-connected-topological-space-0041.json) ## Question 17317: A Clopen Witness Must Also Be Nontrivial - ID: `q-20261014-advance-20261103-r05-connected-topological-space-0042`; number: 17317 - Processing: second_context_reviewed - MKO: [mko-connected-topological-space](/en/mko/mko-connected-topological-space/) - Family: [qf-mod34-connected-clopen-witness](/en/explore/?family=qf-mod34-connected-clopen-witness) - Batch: [batch-20261014-advance-20261103-r05-connected-topological-space-foundations](/en/explore/?batch=batch-20261014-advance-20261103-r05-connected-topological-space-foundations) - [Derivation](/en/questions/q-20261014-advance-20261103-r05-connected-topological-space-0042/) / [Markdown](/en/questions/q-20261014-advance-20261103-r05-connected-topological-space-0042/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261103-r05-connected-topological-space-0042.json) ## Question 17318: A Clopen Witness Must Also Be Nontrivial - ID: `q-20261014-advance-20261103-r05-connected-topological-space-0043`; number: 17318 - Processing: second_context_reviewed - MKO: [mko-connected-topological-space](/en/mko/mko-connected-topological-space/) - Family: [qf-mod34-connected-clopen-witness](/en/explore/?family=qf-mod34-connected-clopen-witness) - Batch: [batch-20261014-advance-20261103-r05-connected-topological-space-foundations](/en/explore/?batch=batch-20261014-advance-20261103-r05-connected-topological-space-foundations) - [Derivation](/en/questions/q-20261014-advance-20261103-r05-connected-topological-space-0043/) / [Markdown](/en/questions/q-20261014-advance-20261103-r05-connected-topological-space-0043/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261103-r05-connected-topological-space-0043.json) ## Question 17319: A Clopen Witness Must Also Be Nontrivial - ID: `q-20261014-advance-20261103-r05-connected-topological-space-0044`; number: 17319 - Processing: second_context_reviewed - MKO: [mko-connected-topological-space](/en/mko/mko-connected-topological-space/) - Family: [qf-mod34-connected-clopen-witness](/en/explore/?family=qf-mod34-connected-clopen-witness) - Batch: [batch-20261014-advance-20261103-r05-connected-topological-space-foundations](/en/explore/?batch=batch-20261014-advance-20261103-r05-connected-topological-space-foundations) - [Derivation](/en/questions/q-20261014-advance-20261103-r05-connected-topological-space-0044/) / [Markdown](/en/questions/q-20261014-advance-20261103-r05-connected-topological-space-0044/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261103-r05-connected-topological-space-0044.json) ## Question 17320: A Clopen Witness Must Also Be Nontrivial - ID: `q-20261014-advance-20261103-r05-connected-topological-space-0045`; number: 17320 - Processing: second_context_reviewed - MKO: [mko-connected-topological-space](/en/mko/mko-connected-topological-space/) - Family: [qf-mod34-connected-clopen-witness](/en/explore/?family=qf-mod34-connected-clopen-witness) - Batch: [batch-20261014-advance-20261103-r05-connected-topological-space-foundations](/en/explore/?batch=batch-20261014-advance-20261103-r05-connected-topological-space-foundations) - [Derivation](/en/questions/q-20261014-advance-20261103-r05-connected-topological-space-0045/) / [Markdown](/en/questions/q-20261014-advance-20261103-r05-connected-topological-space-0045/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261103-r05-connected-topological-space-0045.json) ## Question 17321: A Clopen Witness Must Also Be Nontrivial - ID: `q-20261014-advance-20261103-r05-connected-topological-space-0046`; number: 17321 - Processing: second_context_reviewed - MKO: [mko-connected-topological-space](/en/mko/mko-connected-topological-space/) - Family: [qf-mod34-connected-clopen-witness](/en/explore/?family=qf-mod34-connected-clopen-witness) - Batch: [batch-20261014-advance-20261103-r05-connected-topological-space-foundations](/en/explore/?batch=batch-20261014-advance-20261103-r05-connected-topological-space-foundations) - [Derivation](/en/questions/q-20261014-advance-20261103-r05-connected-topological-space-0046/) / [Markdown](/en/questions/q-20261014-advance-20261103-r05-connected-topological-space-0046/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261103-r05-connected-topological-space-0046.json) ## Question 17322: A Clopen Witness Must Also Be Nontrivial - ID: `q-20261014-advance-20261103-r05-connected-topological-space-0047`; number: 17322 - Processing: second_context_reviewed - MKO: [mko-connected-topological-space](/en/mko/mko-connected-topological-space/) - Family: [qf-mod34-connected-clopen-witness](/en/explore/?family=qf-mod34-connected-clopen-witness) - Batch: [batch-20261014-advance-20261103-r05-connected-topological-space-foundations](/en/explore/?batch=batch-20261014-advance-20261103-r05-connected-topological-space-foundations) - [Derivation](/en/questions/q-20261014-advance-20261103-r05-connected-topological-space-0047/) / [Markdown](/en/questions/q-20261014-advance-20261103-r05-connected-topological-space-0047/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261103-r05-connected-topological-space-0047.json) ## Question 17323: A Clopen Witness Must Also Be Nontrivial - ID: `q-20261014-advance-20261103-r05-connected-topological-space-0048`; number: 17323 - Processing: second_context_reviewed - MKO: [mko-connected-topological-space](/en/mko/mko-connected-topological-space/) - Family: [qf-mod34-connected-clopen-witness](/en/explore/?family=qf-mod34-connected-clopen-witness) - Batch: [batch-20261014-advance-20261103-r05-connected-topological-space-foundations](/en/explore/?batch=batch-20261014-advance-20261103-r05-connected-topological-space-foundations) - [Derivation](/en/questions/q-20261014-advance-20261103-r05-connected-topological-space-0048/) / [Markdown](/en/questions/q-20261014-advance-20261103-r05-connected-topological-space-0048/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261103-r05-connected-topological-space-0048.json) ## Question 17324: A Clopen Witness Must Also Be Nontrivial - ID: `q-20261014-advance-20261103-r05-connected-topological-space-0049`; number: 17324 - Processing: second_context_reviewed - MKO: [mko-connected-topological-space](/en/mko/mko-connected-topological-space/) - Family: [qf-mod34-connected-clopen-witness](/en/explore/?family=qf-mod34-connected-clopen-witness) - Batch: [batch-20261014-advance-20261103-r05-connected-topological-space-foundations](/en/explore/?batch=batch-20261014-advance-20261103-r05-connected-topological-space-foundations) - [Derivation](/en/questions/q-20261014-advance-20261103-r05-connected-topological-space-0049/) / [Markdown](/en/questions/q-20261014-advance-20261103-r05-connected-topological-space-0049/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261103-r05-connected-topological-space-0049.json) ## Question 17325: A Clopen Witness Must Also Be Nontrivial - ID: `q-20261014-advance-20261103-r05-connected-topological-space-0050`; number: 17325 - Processing: second_context_reviewed - MKO: [mko-connected-topological-space](/en/mko/mko-connected-topological-space/) - Family: [qf-mod34-connected-clopen-witness](/en/explore/?family=qf-mod34-connected-clopen-witness) - Batch: [batch-20261014-advance-20261103-r05-connected-topological-space-foundations](/en/explore/?batch=batch-20261014-advance-20261103-r05-connected-topological-space-foundations) - [Derivation](/en/questions/q-20261014-advance-20261103-r05-connected-topological-space-0050/) / [Markdown](/en/questions/q-20261014-advance-20261103-r05-connected-topological-space-0050/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261103-r05-connected-topological-space-0050.json)