General topology Compactness Concept
Limit point compact space
Summary
A limit point compact space is a topological space in which every infinite subset has a limit point. It is the form of compactness that appears in the Bolzano–Weierstrass theorem. Every countably compact space is limit point compact, and the two notions agree for T1 spaces. For metric spaces, it is equivalent to compactness.
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| Tag | E8XKSQY76M |
|---|---|
| URI | m2://E8XKSQY76M |
| Kind | concept |
| Writing | W0 stub |
| MSC | 54D30 |
| Specializes | Topological space |
| Same as | |
| Changed | 2 November 2026 |
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