# OCME · 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 26526: The Union of All Connected Subsets through a Basepoint Is Its Component

- ID: `q-20261015-advance-20261117-r07-topological-connected-component-0001`; number: 26526
- Processing: second_context_reviewed
- MKO: [mko-topological-connected-component](/en/mko/mko-topological-connected-component/)
- Family: [qf-mod48-component-connected-subsets](/en/explore/?family=qf-mod48-component-connected-subsets)
- Batch: [batch-20261015-advance-20261117-r07-topological-connected-component-foundations](/en/explore/?batch=batch-20261015-advance-20261117-r07-topological-connected-component-foundations)
- [Derivation](/en/questions/q-20261015-advance-20261117-r07-topological-connected-component-0001/) / [Markdown](/en/questions/q-20261015-advance-20261117-r07-topological-connected-component-0001/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261117-r07-topological-connected-component-0001.json)

## Question 26527: The Union of All Connected Subsets through a Basepoint Is Its Component

- ID: `q-20261015-advance-20261117-r07-topological-connected-component-0002`; number: 26527
- Processing: second_context_reviewed
- MKO: [mko-topological-connected-component](/en/mko/mko-topological-connected-component/)
- Family: [qf-mod48-component-connected-subsets](/en/explore/?family=qf-mod48-component-connected-subsets)
- Batch: [batch-20261015-advance-20261117-r07-topological-connected-component-foundations](/en/explore/?batch=batch-20261015-advance-20261117-r07-topological-connected-component-foundations)
- [Derivation](/en/questions/q-20261015-advance-20261117-r07-topological-connected-component-0002/) / [Markdown](/en/questions/q-20261015-advance-20261117-r07-topological-connected-component-0002/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261117-r07-topological-connected-component-0002.json)

## Question 26528: The Union of All Connected Subsets through a Basepoint Is Its Component

- ID: `q-20261015-advance-20261117-r07-topological-connected-component-0003`; number: 26528
- Processing: second_context_reviewed
- MKO: [mko-topological-connected-component](/en/mko/mko-topological-connected-component/)
- Family: [qf-mod48-component-connected-subsets](/en/explore/?family=qf-mod48-component-connected-subsets)
- Batch: [batch-20261015-advance-20261117-r07-topological-connected-component-foundations](/en/explore/?batch=batch-20261015-advance-20261117-r07-topological-connected-component-foundations)
- [Derivation](/en/questions/q-20261015-advance-20261117-r07-topological-connected-component-0003/) / [Markdown](/en/questions/q-20261015-advance-20261117-r07-topological-connected-component-0003/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261117-r07-topological-connected-component-0003.json)

## Question 26529: The Union of All Connected Subsets through a Basepoint Is Its Component

- ID: `q-20261015-advance-20261117-r07-topological-connected-component-0004`; number: 26529
- Processing: second_context_reviewed
- MKO: [mko-topological-connected-component](/en/mko/mko-topological-connected-component/)
- Family: [qf-mod48-component-connected-subsets](/en/explore/?family=qf-mod48-component-connected-subsets)
- Batch: [batch-20261015-advance-20261117-r07-topological-connected-component-foundations](/en/explore/?batch=batch-20261015-advance-20261117-r07-topological-connected-component-foundations)
- [Derivation](/en/questions/q-20261015-advance-20261117-r07-topological-connected-component-0004/) / [Markdown](/en/questions/q-20261015-advance-20261117-r07-topological-connected-component-0004/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261117-r07-topological-connected-component-0004.json)

## Question 26530: The Union of All Connected Subsets through a Basepoint Is Its Component

- ID: `q-20261015-advance-20261117-r07-topological-connected-component-0005`; number: 26530
- Processing: second_context_reviewed
- MKO: [mko-topological-connected-component](/en/mko/mko-topological-connected-component/)
- Family: [qf-mod48-component-connected-subsets](/en/explore/?family=qf-mod48-component-connected-subsets)
- Batch: [batch-20261015-advance-20261117-r07-topological-connected-component-foundations](/en/explore/?batch=batch-20261015-advance-20261117-r07-topological-connected-component-foundations)
- [Derivation](/en/questions/q-20261015-advance-20261117-r07-topological-connected-component-0005/) / [Markdown](/en/questions/q-20261015-advance-20261117-r07-topological-connected-component-0005/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261117-r07-topological-connected-component-0005.json)

## Question 26531: The Union of All Connected Subsets through a Basepoint Is Its Component

- ID: `q-20261015-advance-20261117-r07-topological-connected-component-0006`; number: 26531
- Processing: second_context_reviewed
- MKO: [mko-topological-connected-component](/en/mko/mko-topological-connected-component/)
- Family: [qf-mod48-component-connected-subsets](/en/explore/?family=qf-mod48-component-connected-subsets)
- Batch: [batch-20261015-advance-20261117-r07-topological-connected-component-foundations](/en/explore/?batch=batch-20261015-advance-20261117-r07-topological-connected-component-foundations)
- [Derivation](/en/questions/q-20261015-advance-20261117-r07-topological-connected-component-0006/) / [Markdown](/en/questions/q-20261015-advance-20261117-r07-topological-connected-component-0006/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261117-r07-topological-connected-component-0006.json)

## Question 26532: The Union of All Connected Subsets through a Basepoint Is Its Component

- ID: `q-20261015-advance-20261117-r07-topological-connected-component-0007`; number: 26532
- Processing: second_context_reviewed
- MKO: [mko-topological-connected-component](/en/mko/mko-topological-connected-component/)
- Family: [qf-mod48-component-connected-subsets](/en/explore/?family=qf-mod48-component-connected-subsets)
- Batch: [batch-20261015-advance-20261117-r07-topological-connected-component-foundations](/en/explore/?batch=batch-20261015-advance-20261117-r07-topological-connected-component-foundations)
- [Derivation](/en/questions/q-20261015-advance-20261117-r07-topological-connected-component-0007/) / [Markdown](/en/questions/q-20261015-advance-20261117-r07-topological-connected-component-0007/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261117-r07-topological-connected-component-0007.json)

## Question 26533: The Union of All Connected Subsets through a Basepoint Is Its Component

- ID: `q-20261015-advance-20261117-r07-topological-connected-component-0008`; number: 26533
- Processing: second_context_reviewed
- MKO: [mko-topological-connected-component](/en/mko/mko-topological-connected-component/)
- Family: [qf-mod48-component-connected-subsets](/en/explore/?family=qf-mod48-component-connected-subsets)
- Batch: [batch-20261015-advance-20261117-r07-topological-connected-component-foundations](/en/explore/?batch=batch-20261015-advance-20261117-r07-topological-connected-component-foundations)
- [Derivation](/en/questions/q-20261015-advance-20261117-r07-topological-connected-component-0008/) / [Markdown](/en/questions/q-20261015-advance-20261117-r07-topological-connected-component-0008/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261117-r07-topological-connected-component-0008.json)

## Question 26534: The Union of All Connected Subsets through a Basepoint Is Its Component

- ID: `q-20261015-advance-20261117-r07-topological-connected-component-0009`; number: 26534
- Processing: second_context_reviewed
- MKO: [mko-topological-connected-component](/en/mko/mko-topological-connected-component/)
- Family: [qf-mod48-component-connected-subsets](/en/explore/?family=qf-mod48-component-connected-subsets)
- Batch: [batch-20261015-advance-20261117-r07-topological-connected-component-foundations](/en/explore/?batch=batch-20261015-advance-20261117-r07-topological-connected-component-foundations)
- [Derivation](/en/questions/q-20261015-advance-20261117-r07-topological-connected-component-0009/) / [Markdown](/en/questions/q-20261015-advance-20261117-r07-topological-connected-component-0009/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261117-r07-topological-connected-component-0009.json)

## Question 26535: The Union of All Connected Subsets through a Basepoint Is Its Component

- ID: `q-20261015-advance-20261117-r07-topological-connected-component-0010`; number: 26535
- Processing: second_context_reviewed
- MKO: [mko-topological-connected-component](/en/mko/mko-topological-connected-component/)
- Family: [qf-mod48-component-connected-subsets](/en/explore/?family=qf-mod48-component-connected-subsets)
- Batch: [batch-20261015-advance-20261117-r07-topological-connected-component-foundations](/en/explore/?batch=batch-20261015-advance-20261117-r07-topological-connected-component-foundations)
- [Derivation](/en/questions/q-20261015-advance-20261117-r07-topological-connected-component-0010/) / [Markdown](/en/questions/q-20261015-advance-20261117-r07-topological-connected-component-0010/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261117-r07-topological-connected-component-0010.json)

## Question 26536: The Union of All Connected Subsets through a Basepoint Is Its Component

- ID: `q-20261015-advance-20261117-r07-topological-connected-component-0011`; number: 26536
- Processing: second_context_reviewed
- MKO: [mko-topological-connected-component](/en/mko/mko-topological-connected-component/)
- Family: [qf-mod48-component-connected-subsets](/en/explore/?family=qf-mod48-component-connected-subsets)
- Batch: [batch-20261015-advance-20261117-r07-topological-connected-component-foundations](/en/explore/?batch=batch-20261015-advance-20261117-r07-topological-connected-component-foundations)
- [Derivation](/en/questions/q-20261015-advance-20261117-r07-topological-connected-component-0011/) / [Markdown](/en/questions/q-20261015-advance-20261117-r07-topological-connected-component-0011/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261117-r07-topological-connected-component-0011.json)

## Question 26537: The Union of All Connected Subsets through a Basepoint Is Its Component

- ID: `q-20261015-advance-20261117-r07-topological-connected-component-0012`; number: 26537
- Processing: second_context_reviewed
- MKO: [mko-topological-connected-component](/en/mko/mko-topological-connected-component/)
- Family: [qf-mod48-component-connected-subsets](/en/explore/?family=qf-mod48-component-connected-subsets)
- Batch: [batch-20261015-advance-20261117-r07-topological-connected-component-foundations](/en/explore/?batch=batch-20261015-advance-20261117-r07-topological-connected-component-foundations)
- [Derivation](/en/questions/q-20261015-advance-20261117-r07-topological-connected-component-0012/) / [Markdown](/en/questions/q-20261015-advance-20261117-r07-topological-connected-component-0012/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261117-r07-topological-connected-component-0012.json)

## Question 26538: The Union of All Connected Subsets through a Basepoint Is Its Component

- ID: `q-20261015-advance-20261117-r07-topological-connected-component-0013`; number: 26538
- Processing: second_context_reviewed
- MKO: [mko-topological-connected-component](/en/mko/mko-topological-connected-component/)
- Family: [qf-mod48-component-connected-subsets](/en/explore/?family=qf-mod48-component-connected-subsets)
- Batch: [batch-20261015-advance-20261117-r07-topological-connected-component-foundations](/en/explore/?batch=batch-20261015-advance-20261117-r07-topological-connected-component-foundations)
- [Derivation](/en/questions/q-20261015-advance-20261117-r07-topological-connected-component-0013/) / [Markdown](/en/questions/q-20261015-advance-20261117-r07-topological-connected-component-0013/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261117-r07-topological-connected-component-0013.json)

## Question 26539: The Union of All Connected Subsets through a Basepoint Is Its Component

- ID: `q-20261015-advance-20261117-r07-topological-connected-component-0014`; number: 26539
- Processing: second_context_reviewed
- MKO: [mko-topological-connected-component](/en/mko/mko-topological-connected-component/)
- Family: [qf-mod48-component-connected-subsets](/en/explore/?family=qf-mod48-component-connected-subsets)
- Batch: [batch-20261015-advance-20261117-r07-topological-connected-component-foundations](/en/explore/?batch=batch-20261015-advance-20261117-r07-topological-connected-component-foundations)
- [Derivation](/en/questions/q-20261015-advance-20261117-r07-topological-connected-component-0014/) / [Markdown](/en/questions/q-20261015-advance-20261117-r07-topological-connected-component-0014/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261117-r07-topological-connected-component-0014.json)

## Question 26540: The Union of All Connected Subsets through a Basepoint Is Its Component

- ID: `q-20261015-advance-20261117-r07-topological-connected-component-0015`; number: 26540
- Processing: second_context_reviewed
- MKO: [mko-topological-connected-component](/en/mko/mko-topological-connected-component/)
- Family: [qf-mod48-component-connected-subsets](/en/explore/?family=qf-mod48-component-connected-subsets)
- Batch: [batch-20261015-advance-20261117-r07-topological-connected-component-foundations](/en/explore/?batch=batch-20261015-advance-20261117-r07-topological-connected-component-foundations)
- [Derivation](/en/questions/q-20261015-advance-20261117-r07-topological-connected-component-0015/) / [Markdown](/en/questions/q-20261015-advance-20261117-r07-topological-connected-component-0015/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261117-r07-topological-connected-component-0015.json)

## Question 26541: The Union of All Connected Subsets through a Basepoint Is Its Component

- ID: `q-20261015-advance-20261117-r07-topological-connected-component-0016`; number: 26541
- Processing: second_context_reviewed
- MKO: [mko-topological-connected-component](/en/mko/mko-topological-connected-component/)
- Family: [qf-mod48-component-connected-subsets](/en/explore/?family=qf-mod48-component-connected-subsets)
- Batch: [batch-20261015-advance-20261117-r07-topological-connected-component-foundations](/en/explore/?batch=batch-20261015-advance-20261117-r07-topological-connected-component-foundations)
- [Derivation](/en/questions/q-20261015-advance-20261117-r07-topological-connected-component-0016/) / [Markdown](/en/questions/q-20261015-advance-20261117-r07-topological-connected-component-0016/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261117-r07-topological-connected-component-0016.json)

## Question 26542: The Union of All Connected Subsets through a Basepoint Is Its Component

- ID: `q-20261015-advance-20261117-r07-topological-connected-component-0017`; number: 26542
- Processing: second_context_reviewed
- MKO: [mko-topological-connected-component](/en/mko/mko-topological-connected-component/)
- Family: [qf-mod48-component-connected-subsets](/en/explore/?family=qf-mod48-component-connected-subsets)
- Batch: [batch-20261015-advance-20261117-r07-topological-connected-component-foundations](/en/explore/?batch=batch-20261015-advance-20261117-r07-topological-connected-component-foundations)
- [Derivation](/en/questions/q-20261015-advance-20261117-r07-topological-connected-component-0017/) / [Markdown](/en/questions/q-20261015-advance-20261117-r07-topological-connected-component-0017/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261117-r07-topological-connected-component-0017.json)

## Question 26543: The Union of All Connected Subsets through a Basepoint Is Its Component

- ID: `q-20261015-advance-20261117-r07-topological-connected-component-0018`; number: 26543
- Processing: second_context_reviewed
- MKO: [mko-topological-connected-component](/en/mko/mko-topological-connected-component/)
- Family: [qf-mod48-component-connected-subsets](/en/explore/?family=qf-mod48-component-connected-subsets)
- Batch: [batch-20261015-advance-20261117-r07-topological-connected-component-foundations](/en/explore/?batch=batch-20261015-advance-20261117-r07-topological-connected-component-foundations)
- [Derivation](/en/questions/q-20261015-advance-20261117-r07-topological-connected-component-0018/) / [Markdown](/en/questions/q-20261015-advance-20261117-r07-topological-connected-component-0018/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261117-r07-topological-connected-component-0018.json)

## Question 26544: The Union of All Connected Subsets through a Basepoint Is Its Component

- ID: `q-20261015-advance-20261117-r07-topological-connected-component-0019`; number: 26544
- Processing: second_context_reviewed
- MKO: [mko-topological-connected-component](/en/mko/mko-topological-connected-component/)
- Family: [qf-mod48-component-connected-subsets](/en/explore/?family=qf-mod48-component-connected-subsets)
- Batch: [batch-20261015-advance-20261117-r07-topological-connected-component-foundations](/en/explore/?batch=batch-20261015-advance-20261117-r07-topological-connected-component-foundations)
- [Derivation](/en/questions/q-20261015-advance-20261117-r07-topological-connected-component-0019/) / [Markdown](/en/questions/q-20261015-advance-20261117-r07-topological-connected-component-0019/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261117-r07-topological-connected-component-0019.json)

## Question 26545: The Union of All Connected Subsets through a Basepoint Is Its Component

- ID: `q-20261015-advance-20261117-r07-topological-connected-component-0020`; number: 26545
- Processing: second_context_reviewed
- MKO: [mko-topological-connected-component](/en/mko/mko-topological-connected-component/)
- Family: [qf-mod48-component-connected-subsets](/en/explore/?family=qf-mod48-component-connected-subsets)
- Batch: [batch-20261015-advance-20261117-r07-topological-connected-component-foundations](/en/explore/?batch=batch-20261015-advance-20261117-r07-topological-connected-component-foundations)
- [Derivation](/en/questions/q-20261015-advance-20261117-r07-topological-connected-component-0020/) / [Markdown](/en/questions/q-20261015-advance-20261117-r07-topological-connected-component-0020/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261117-r07-topological-connected-component-0020.json)

## Question 26546: The Union of All Connected Subsets through a Basepoint Is Its Component

- ID: `q-20261015-advance-20261117-r07-topological-connected-component-0021`; number: 26546
- Processing: second_context_reviewed
- MKO: [mko-topological-connected-component](/en/mko/mko-topological-connected-component/)
- Family: [qf-mod48-component-connected-subsets](/en/explore/?family=qf-mod48-component-connected-subsets)
- Batch: [batch-20261015-advance-20261117-r07-topological-connected-component-foundations](/en/explore/?batch=batch-20261015-advance-20261117-r07-topological-connected-component-foundations)
- [Derivation](/en/questions/q-20261015-advance-20261117-r07-topological-connected-component-0021/) / [Markdown](/en/questions/q-20261015-advance-20261117-r07-topological-connected-component-0021/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261117-r07-topological-connected-component-0021.json)

## Question 26547: The Union of All Connected Subsets through a Basepoint Is Its Component

- ID: `q-20261015-advance-20261117-r07-topological-connected-component-0022`; number: 26547
- Processing: second_context_reviewed
- MKO: [mko-topological-connected-component](/en/mko/mko-topological-connected-component/)
- Family: [qf-mod48-component-connected-subsets](/en/explore/?family=qf-mod48-component-connected-subsets)
- Batch: [batch-20261015-advance-20261117-r07-topological-connected-component-foundations](/en/explore/?batch=batch-20261015-advance-20261117-r07-topological-connected-component-foundations)
- [Derivation](/en/questions/q-20261015-advance-20261117-r07-topological-connected-component-0022/) / [Markdown](/en/questions/q-20261015-advance-20261117-r07-topological-connected-component-0022/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261117-r07-topological-connected-component-0022.json)

## Question 26548: The Union of All Connected Subsets through a Basepoint Is Its Component

- ID: `q-20261015-advance-20261117-r07-topological-connected-component-0023`; number: 26548
- Processing: second_context_reviewed
- MKO: [mko-topological-connected-component](/en/mko/mko-topological-connected-component/)
- Family: [qf-mod48-component-connected-subsets](/en/explore/?family=qf-mod48-component-connected-subsets)
- Batch: [batch-20261015-advance-20261117-r07-topological-connected-component-foundations](/en/explore/?batch=batch-20261015-advance-20261117-r07-topological-connected-component-foundations)
- [Derivation](/en/questions/q-20261015-advance-20261117-r07-topological-connected-component-0023/) / [Markdown](/en/questions/q-20261015-advance-20261117-r07-topological-connected-component-0023/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261117-r07-topological-connected-component-0023.json)

## Question 26549: The Union of All Connected Subsets through a Basepoint Is Its Component

- ID: `q-20261015-advance-20261117-r07-topological-connected-component-0024`; number: 26549
- Processing: second_context_reviewed
- MKO: [mko-topological-connected-component](/en/mko/mko-topological-connected-component/)
- Family: [qf-mod48-component-connected-subsets](/en/explore/?family=qf-mod48-component-connected-subsets)
- Batch: [batch-20261015-advance-20261117-r07-topological-connected-component-foundations](/en/explore/?batch=batch-20261015-advance-20261117-r07-topological-connected-component-foundations)
- [Derivation](/en/questions/q-20261015-advance-20261117-r07-topological-connected-component-0024/) / [Markdown](/en/questions/q-20261015-advance-20261117-r07-topological-connected-component-0024/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261117-r07-topological-connected-component-0024.json)

## Question 26550: The Union of All Connected Subsets through a Basepoint Is Its Component

- ID: `q-20261015-advance-20261117-r07-topological-connected-component-0025`; number: 26550
- Processing: second_context_reviewed
- MKO: [mko-topological-connected-component](/en/mko/mko-topological-connected-component/)
- Family: [qf-mod48-component-connected-subsets](/en/explore/?family=qf-mod48-component-connected-subsets)
- Batch: [batch-20261015-advance-20261117-r07-topological-connected-component-foundations](/en/explore/?batch=batch-20261015-advance-20261117-r07-topological-connected-component-foundations)
- [Derivation](/en/questions/q-20261015-advance-20261117-r07-topological-connected-component-0025/) / [Markdown](/en/questions/q-20261015-advance-20261117-r07-topological-connected-component-0025/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261117-r07-topological-connected-component-0025.json)