General topology Compactness Concept
Countably compact space
Summary
A countably compact space is a topological space in which every countable open cover has a finite subcover. It is a weakening of compactness that is equivalent to the statement that every sequence has a cluster point. Compact spaces and sequentially compact spaces are countably compact. For metric spaces, countable compactness, compactness and sequential compactness all coincide.
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| Tag | S3N3CHZV89 |
|---|---|
| URI | m2://S3N3CHZV89 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 54D30 |
| Specializes | Limit point compact space |
| Same as | |
| Changed | 2 November 2026 |
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