# 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.

100 results; page 2/4.

## Question 26726: Each Coordinate Projection Has Open Preimages for Every Factor Open

- ID: `q-20261015-advance-20261117-r04-finite-product-topology-0026`; number: 26726
- Processing: second_context_reviewed
- MKO: [mko-finite-product-topology](/en/mko/mko-finite-product-topology/)
- Family: [qf-mod48-product-projection-continuity](/en/explore/?family=qf-mod48-product-projection-continuity)
- Batch: [batch-20261015-advance-20261117-r04-finite-product-topology-foundations](/en/explore/?batch=batch-20261015-advance-20261117-r04-finite-product-topology-foundations)
- [Derivation](/en/questions/q-20261015-advance-20261117-r04-finite-product-topology-0026/) / [Markdown](/en/questions/q-20261015-advance-20261117-r04-finite-product-topology-0026/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261117-r04-finite-product-topology-0026.json)

## Question 26727: Each Coordinate Projection Has Open Preimages for Every Factor Open

- ID: `q-20261015-advance-20261117-r04-finite-product-topology-0027`; number: 26727
- Processing: second_context_reviewed
- MKO: [mko-finite-product-topology](/en/mko/mko-finite-product-topology/)
- Family: [qf-mod48-product-projection-continuity](/en/explore/?family=qf-mod48-product-projection-continuity)
- Batch: [batch-20261015-advance-20261117-r04-finite-product-topology-foundations](/en/explore/?batch=batch-20261015-advance-20261117-r04-finite-product-topology-foundations)
- [Derivation](/en/questions/q-20261015-advance-20261117-r04-finite-product-topology-0027/) / [Markdown](/en/questions/q-20261015-advance-20261117-r04-finite-product-topology-0027/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261117-r04-finite-product-topology-0027.json)

## Question 26728: Each Coordinate Projection Has Open Preimages for Every Factor Open

- ID: `q-20261015-advance-20261117-r04-finite-product-topology-0028`; number: 26728
- Processing: second_context_reviewed
- MKO: [mko-finite-product-topology](/en/mko/mko-finite-product-topology/)
- Family: [qf-mod48-product-projection-continuity](/en/explore/?family=qf-mod48-product-projection-continuity)
- Batch: [batch-20261015-advance-20261117-r04-finite-product-topology-foundations](/en/explore/?batch=batch-20261015-advance-20261117-r04-finite-product-topology-foundations)
- [Derivation](/en/questions/q-20261015-advance-20261117-r04-finite-product-topology-0028/) / [Markdown](/en/questions/q-20261015-advance-20261117-r04-finite-product-topology-0028/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261117-r04-finite-product-topology-0028.json)

## Question 26729: Each Coordinate Projection Has Open Preimages for Every Factor Open

- ID: `q-20261015-advance-20261117-r04-finite-product-topology-0029`; number: 26729
- Processing: second_context_reviewed
- MKO: [mko-finite-product-topology](/en/mko/mko-finite-product-topology/)
- Family: [qf-mod48-product-projection-continuity](/en/explore/?family=qf-mod48-product-projection-continuity)
- Batch: [batch-20261015-advance-20261117-r04-finite-product-topology-foundations](/en/explore/?batch=batch-20261015-advance-20261117-r04-finite-product-topology-foundations)
- [Derivation](/en/questions/q-20261015-advance-20261117-r04-finite-product-topology-0029/) / [Markdown](/en/questions/q-20261015-advance-20261117-r04-finite-product-topology-0029/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261117-r04-finite-product-topology-0029.json)

## Question 26730: Each Coordinate Projection Has Open Preimages for Every Factor Open

- ID: `q-20261015-advance-20261117-r04-finite-product-topology-0030`; number: 26730
- Processing: second_context_reviewed
- MKO: [mko-finite-product-topology](/en/mko/mko-finite-product-topology/)
- Family: [qf-mod48-product-projection-continuity](/en/explore/?family=qf-mod48-product-projection-continuity)
- Batch: [batch-20261015-advance-20261117-r04-finite-product-topology-foundations](/en/explore/?batch=batch-20261015-advance-20261117-r04-finite-product-topology-foundations)
- [Derivation](/en/questions/q-20261015-advance-20261117-r04-finite-product-topology-0030/) / [Markdown](/en/questions/q-20261015-advance-20261117-r04-finite-product-topology-0030/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261117-r04-finite-product-topology-0030.json)

## Question 26731: Each Coordinate Projection Has Open Preimages for Every Factor Open

- ID: `q-20261015-advance-20261117-r04-finite-product-topology-0031`; number: 26731
- Processing: second_context_reviewed
- MKO: [mko-finite-product-topology](/en/mko/mko-finite-product-topology/)
- Family: [qf-mod48-product-projection-continuity](/en/explore/?family=qf-mod48-product-projection-continuity)
- Batch: [batch-20261015-advance-20261117-r04-finite-product-topology-foundations](/en/explore/?batch=batch-20261015-advance-20261117-r04-finite-product-topology-foundations)
- [Derivation](/en/questions/q-20261015-advance-20261117-r04-finite-product-topology-0031/) / [Markdown](/en/questions/q-20261015-advance-20261117-r04-finite-product-topology-0031/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261117-r04-finite-product-topology-0031.json)

## Question 26732: Each Coordinate Projection Has Open Preimages for Every Factor Open

- ID: `q-20261015-advance-20261117-r04-finite-product-topology-0032`; number: 26732
- Processing: second_context_reviewed
- MKO: [mko-finite-product-topology](/en/mko/mko-finite-product-topology/)
- Family: [qf-mod48-product-projection-continuity](/en/explore/?family=qf-mod48-product-projection-continuity)
- Batch: [batch-20261015-advance-20261117-r04-finite-product-topology-foundations](/en/explore/?batch=batch-20261015-advance-20261117-r04-finite-product-topology-foundations)
- [Derivation](/en/questions/q-20261015-advance-20261117-r04-finite-product-topology-0032/) / [Markdown](/en/questions/q-20261015-advance-20261117-r04-finite-product-topology-0032/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261117-r04-finite-product-topology-0032.json)

## Question 26733: Each Coordinate Projection Has Open Preimages for Every Factor Open

- ID: `q-20261015-advance-20261117-r04-finite-product-topology-0033`; number: 26733
- Processing: second_context_reviewed
- MKO: [mko-finite-product-topology](/en/mko/mko-finite-product-topology/)
- Family: [qf-mod48-product-projection-continuity](/en/explore/?family=qf-mod48-product-projection-continuity)
- Batch: [batch-20261015-advance-20261117-r04-finite-product-topology-foundations](/en/explore/?batch=batch-20261015-advance-20261117-r04-finite-product-topology-foundations)
- [Derivation](/en/questions/q-20261015-advance-20261117-r04-finite-product-topology-0033/) / [Markdown](/en/questions/q-20261015-advance-20261117-r04-finite-product-topology-0033/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261117-r04-finite-product-topology-0033.json)

## Question 26734: Each Coordinate Projection Has Open Preimages for Every Factor Open

- ID: `q-20261015-advance-20261117-r04-finite-product-topology-0034`; number: 26734
- Processing: second_context_reviewed
- MKO: [mko-finite-product-topology](/en/mko/mko-finite-product-topology/)
- Family: [qf-mod48-product-projection-continuity](/en/explore/?family=qf-mod48-product-projection-continuity)
- Batch: [batch-20261015-advance-20261117-r04-finite-product-topology-foundations](/en/explore/?batch=batch-20261015-advance-20261117-r04-finite-product-topology-foundations)
- [Derivation](/en/questions/q-20261015-advance-20261117-r04-finite-product-topology-0034/) / [Markdown](/en/questions/q-20261015-advance-20261117-r04-finite-product-topology-0034/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261117-r04-finite-product-topology-0034.json)

## Question 26735: Each Coordinate Projection Has Open Preimages for Every Factor Open

- ID: `q-20261015-advance-20261117-r04-finite-product-topology-0035`; number: 26735
- Processing: second_context_reviewed
- MKO: [mko-finite-product-topology](/en/mko/mko-finite-product-topology/)
- Family: [qf-mod48-product-projection-continuity](/en/explore/?family=qf-mod48-product-projection-continuity)
- Batch: [batch-20261015-advance-20261117-r04-finite-product-topology-foundations](/en/explore/?batch=batch-20261015-advance-20261117-r04-finite-product-topology-foundations)
- [Derivation](/en/questions/q-20261015-advance-20261117-r04-finite-product-topology-0035/) / [Markdown](/en/questions/q-20261015-advance-20261117-r04-finite-product-topology-0035/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261117-r04-finite-product-topology-0035.json)

## Question 26736: Each Coordinate Projection Has Open Preimages for Every Factor Open

- ID: `q-20261015-advance-20261117-r04-finite-product-topology-0036`; number: 26736
- Processing: second_context_reviewed
- MKO: [mko-finite-product-topology](/en/mko/mko-finite-product-topology/)
- Family: [qf-mod48-product-projection-continuity](/en/explore/?family=qf-mod48-product-projection-continuity)
- Batch: [batch-20261015-advance-20261117-r04-finite-product-topology-foundations](/en/explore/?batch=batch-20261015-advance-20261117-r04-finite-product-topology-foundations)
- [Derivation](/en/questions/q-20261015-advance-20261117-r04-finite-product-topology-0036/) / [Markdown](/en/questions/q-20261015-advance-20261117-r04-finite-product-topology-0036/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261117-r04-finite-product-topology-0036.json)

## Question 26737: Each Coordinate Projection Has Open Preimages for Every Factor Open

- ID: `q-20261015-advance-20261117-r04-finite-product-topology-0037`; number: 26737
- Processing: second_context_reviewed
- MKO: [mko-finite-product-topology](/en/mko/mko-finite-product-topology/)
- Family: [qf-mod48-product-projection-continuity](/en/explore/?family=qf-mod48-product-projection-continuity)
- Batch: [batch-20261015-advance-20261117-r04-finite-product-topology-foundations](/en/explore/?batch=batch-20261015-advance-20261117-r04-finite-product-topology-foundations)
- [Derivation](/en/questions/q-20261015-advance-20261117-r04-finite-product-topology-0037/) / [Markdown](/en/questions/q-20261015-advance-20261117-r04-finite-product-topology-0037/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261117-r04-finite-product-topology-0037.json)

## Question 26738: Each Coordinate Projection Has Open Preimages for Every Factor Open

- ID: `q-20261015-advance-20261117-r04-finite-product-topology-0038`; number: 26738
- Processing: second_context_reviewed
- MKO: [mko-finite-product-topology](/en/mko/mko-finite-product-topology/)
- Family: [qf-mod48-product-projection-continuity](/en/explore/?family=qf-mod48-product-projection-continuity)
- Batch: [batch-20261015-advance-20261117-r04-finite-product-topology-foundations](/en/explore/?batch=batch-20261015-advance-20261117-r04-finite-product-topology-foundations)
- [Derivation](/en/questions/q-20261015-advance-20261117-r04-finite-product-topology-0038/) / [Markdown](/en/questions/q-20261015-advance-20261117-r04-finite-product-topology-0038/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261117-r04-finite-product-topology-0038.json)

## Question 26739: Each Coordinate Projection Has Open Preimages for Every Factor Open

- ID: `q-20261015-advance-20261117-r04-finite-product-topology-0039`; number: 26739
- Processing: second_context_reviewed
- MKO: [mko-finite-product-topology](/en/mko/mko-finite-product-topology/)
- Family: [qf-mod48-product-projection-continuity](/en/explore/?family=qf-mod48-product-projection-continuity)
- Batch: [batch-20261015-advance-20261117-r04-finite-product-topology-foundations](/en/explore/?batch=batch-20261015-advance-20261117-r04-finite-product-topology-foundations)
- [Derivation](/en/questions/q-20261015-advance-20261117-r04-finite-product-topology-0039/) / [Markdown](/en/questions/q-20261015-advance-20261117-r04-finite-product-topology-0039/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261117-r04-finite-product-topology-0039.json)

## Question 26740: Each Coordinate Projection Has Open Preimages for Every Factor Open

- ID: `q-20261015-advance-20261117-r04-finite-product-topology-0040`; number: 26740
- Processing: second_context_reviewed
- MKO: [mko-finite-product-topology](/en/mko/mko-finite-product-topology/)
- Family: [qf-mod48-product-projection-continuity](/en/explore/?family=qf-mod48-product-projection-continuity)
- Batch: [batch-20261015-advance-20261117-r04-finite-product-topology-foundations](/en/explore/?batch=batch-20261015-advance-20261117-r04-finite-product-topology-foundations)
- [Derivation](/en/questions/q-20261015-advance-20261117-r04-finite-product-topology-0040/) / [Markdown](/en/questions/q-20261015-advance-20261117-r04-finite-product-topology-0040/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261117-r04-finite-product-topology-0040.json)

## Question 26741: Each Coordinate Projection Has Open Preimages for Every Factor Open

- ID: `q-20261015-advance-20261117-r04-finite-product-topology-0041`; number: 26741
- Processing: second_context_reviewed
- MKO: [mko-finite-product-topology](/en/mko/mko-finite-product-topology/)
- Family: [qf-mod48-product-projection-continuity](/en/explore/?family=qf-mod48-product-projection-continuity)
- Batch: [batch-20261015-advance-20261117-r04-finite-product-topology-foundations](/en/explore/?batch=batch-20261015-advance-20261117-r04-finite-product-topology-foundations)
- [Derivation](/en/questions/q-20261015-advance-20261117-r04-finite-product-topology-0041/) / [Markdown](/en/questions/q-20261015-advance-20261117-r04-finite-product-topology-0041/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261117-r04-finite-product-topology-0041.json)

## Question 26742: Each Coordinate Projection Has Open Preimages for Every Factor Open

- ID: `q-20261015-advance-20261117-r04-finite-product-topology-0042`; number: 26742
- Processing: second_context_reviewed
- MKO: [mko-finite-product-topology](/en/mko/mko-finite-product-topology/)
- Family: [qf-mod48-product-projection-continuity](/en/explore/?family=qf-mod48-product-projection-continuity)
- Batch: [batch-20261015-advance-20261117-r04-finite-product-topology-foundations](/en/explore/?batch=batch-20261015-advance-20261117-r04-finite-product-topology-foundations)
- [Derivation](/en/questions/q-20261015-advance-20261117-r04-finite-product-topology-0042/) / [Markdown](/en/questions/q-20261015-advance-20261117-r04-finite-product-topology-0042/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261117-r04-finite-product-topology-0042.json)

## Question 26743: Each Coordinate Projection Has Open Preimages for Every Factor Open

- ID: `q-20261015-advance-20261117-r04-finite-product-topology-0043`; number: 26743
- Processing: second_context_reviewed
- MKO: [mko-finite-product-topology](/en/mko/mko-finite-product-topology/)
- Family: [qf-mod48-product-projection-continuity](/en/explore/?family=qf-mod48-product-projection-continuity)
- Batch: [batch-20261015-advance-20261117-r04-finite-product-topology-foundations](/en/explore/?batch=batch-20261015-advance-20261117-r04-finite-product-topology-foundations)
- [Derivation](/en/questions/q-20261015-advance-20261117-r04-finite-product-topology-0043/) / [Markdown](/en/questions/q-20261015-advance-20261117-r04-finite-product-topology-0043/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261117-r04-finite-product-topology-0043.json)

## Question 26744: Each Coordinate Projection Has Open Preimages for Every Factor Open

- ID: `q-20261015-advance-20261117-r04-finite-product-topology-0044`; number: 26744
- Processing: second_context_reviewed
- MKO: [mko-finite-product-topology](/en/mko/mko-finite-product-topology/)
- Family: [qf-mod48-product-projection-continuity](/en/explore/?family=qf-mod48-product-projection-continuity)
- Batch: [batch-20261015-advance-20261117-r04-finite-product-topology-foundations](/en/explore/?batch=batch-20261015-advance-20261117-r04-finite-product-topology-foundations)
- [Derivation](/en/questions/q-20261015-advance-20261117-r04-finite-product-topology-0044/) / [Markdown](/en/questions/q-20261015-advance-20261117-r04-finite-product-topology-0044/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261117-r04-finite-product-topology-0044.json)

## Question 26745: Each Coordinate Projection Has Open Preimages for Every Factor Open

- ID: `q-20261015-advance-20261117-r04-finite-product-topology-0045`; number: 26745
- Processing: second_context_reviewed
- MKO: [mko-finite-product-topology](/en/mko/mko-finite-product-topology/)
- Family: [qf-mod48-product-projection-continuity](/en/explore/?family=qf-mod48-product-projection-continuity)
- Batch: [batch-20261015-advance-20261117-r04-finite-product-topology-foundations](/en/explore/?batch=batch-20261015-advance-20261117-r04-finite-product-topology-foundations)
- [Derivation](/en/questions/q-20261015-advance-20261117-r04-finite-product-topology-0045/) / [Markdown](/en/questions/q-20261015-advance-20261117-r04-finite-product-topology-0045/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261117-r04-finite-product-topology-0045.json)

## Question 26746: Each Coordinate Projection Has Open Preimages for Every Factor Open

- ID: `q-20261015-advance-20261117-r04-finite-product-topology-0046`; number: 26746
- Processing: second_context_reviewed
- MKO: [mko-finite-product-topology](/en/mko/mko-finite-product-topology/)
- Family: [qf-mod48-product-projection-continuity](/en/explore/?family=qf-mod48-product-projection-continuity)
- Batch: [batch-20261015-advance-20261117-r04-finite-product-topology-foundations](/en/explore/?batch=batch-20261015-advance-20261117-r04-finite-product-topology-foundations)
- [Derivation](/en/questions/q-20261015-advance-20261117-r04-finite-product-topology-0046/) / [Markdown](/en/questions/q-20261015-advance-20261117-r04-finite-product-topology-0046/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261117-r04-finite-product-topology-0046.json)

## Question 26747: Each Coordinate Projection Has Open Preimages for Every Factor Open

- ID: `q-20261015-advance-20261117-r04-finite-product-topology-0047`; number: 26747
- Processing: second_context_reviewed
- MKO: [mko-finite-product-topology](/en/mko/mko-finite-product-topology/)
- Family: [qf-mod48-product-projection-continuity](/en/explore/?family=qf-mod48-product-projection-continuity)
- Batch: [batch-20261015-advance-20261117-r04-finite-product-topology-foundations](/en/explore/?batch=batch-20261015-advance-20261117-r04-finite-product-topology-foundations)
- [Derivation](/en/questions/q-20261015-advance-20261117-r04-finite-product-topology-0047/) / [Markdown](/en/questions/q-20261015-advance-20261117-r04-finite-product-topology-0047/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261117-r04-finite-product-topology-0047.json)

## Question 26748: Each Coordinate Projection Has Open Preimages for Every Factor Open

- ID: `q-20261015-advance-20261117-r04-finite-product-topology-0048`; number: 26748
- Processing: second_context_reviewed
- MKO: [mko-finite-product-topology](/en/mko/mko-finite-product-topology/)
- Family: [qf-mod48-product-projection-continuity](/en/explore/?family=qf-mod48-product-projection-continuity)
- Batch: [batch-20261015-advance-20261117-r04-finite-product-topology-foundations](/en/explore/?batch=batch-20261015-advance-20261117-r04-finite-product-topology-foundations)
- [Derivation](/en/questions/q-20261015-advance-20261117-r04-finite-product-topology-0048/) / [Markdown](/en/questions/q-20261015-advance-20261117-r04-finite-product-topology-0048/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261117-r04-finite-product-topology-0048.json)

## Question 26749: Each Coordinate Projection Has Open Preimages for Every Factor Open

- ID: `q-20261015-advance-20261117-r04-finite-product-topology-0049`; number: 26749
- Processing: second_context_reviewed
- MKO: [mko-finite-product-topology](/en/mko/mko-finite-product-topology/)
- Family: [qf-mod48-product-projection-continuity](/en/explore/?family=qf-mod48-product-projection-continuity)
- Batch: [batch-20261015-advance-20261117-r04-finite-product-topology-foundations](/en/explore/?batch=batch-20261015-advance-20261117-r04-finite-product-topology-foundations)
- [Derivation](/en/questions/q-20261015-advance-20261117-r04-finite-product-topology-0049/) / [Markdown](/en/questions/q-20261015-advance-20261117-r04-finite-product-topology-0049/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261117-r04-finite-product-topology-0049.json)

## Question 26750: Each Coordinate Projection Has Open Preimages for Every Factor Open

- ID: `q-20261015-advance-20261117-r04-finite-product-topology-0050`; number: 26750
- Processing: second_context_reviewed
- MKO: [mko-finite-product-topology](/en/mko/mko-finite-product-topology/)
- Family: [qf-mod48-product-projection-continuity](/en/explore/?family=qf-mod48-product-projection-continuity)
- Batch: [batch-20261015-advance-20261117-r04-finite-product-topology-foundations](/en/explore/?batch=batch-20261015-advance-20261117-r04-finite-product-topology-foundations)
- [Derivation](/en/questions/q-20261015-advance-20261117-r04-finite-product-topology-0050/) / [Markdown](/en/questions/q-20261015-advance-20261117-r04-finite-product-topology-0050/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261117-r04-finite-product-topology-0050.json)

[Next](/en/explore/index.md?mko=mko-finite-product-topology&page=3)