A finite subcover is a subcover with finitely many members, including possibly none when K is the empty set. Requiring a finite subcover for every open cover is the definition of compactness.
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- Closed subset of a compact space
- Compact space
- Compact subset of a Hausdorff space
- Continuous image of a compact space
- Every subset of a cofinite space is compact
- Finite intersection characterization of compactness
- Finite subcover
- Noncompactness after collapsing a countable real subset
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