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Homework Statement
Let X be a topological space. Let A be compact in X. Let B be contained in A. Let B also be closed in X. Is it always true that B is compact in X?
Is a Closed Subset of a Compact Set Always Compact?
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Let X be a topological space. Let A be compact in X. Let B be contained in A. Let B also be closed in X. Is it always true that B is compact in X?
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B will be compact in A, and consequently in X as well.
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