Compact space
= Compact space
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= Quasi-compact topological space
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= Quasi-compactness
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= Quasi-compact
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= Compact subset
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= Compact
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= Compact set
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= Compactness
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A topological space is compact when every open cover has a finite subcover. Every closed subspace of a compact space is compact. This open-cover definition does not require the space to be Hausdorff; in algebraic geometry it is often called quasi-compactness.