In Hausdorff spaces, compact sets are closed
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How to prove that a compact set in a Hausdorff topological space is closed?
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A closed set in $(A, \mathcal T_A)$ that is not closed in $(X, \mathcal T)$
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If $X$ is an infinite set, then $X$ with the discrete topology is not compact
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Closed subset of compact set is compact
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When is the vector space of continuous functions on a compact Hausdorff space finite dimensional?
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prove that every infinite subset of compact set H has a limit point (Explanation)
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Interior of closure of open set in topological space
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Help completing a proof regarding an infinite family of nested closed subsets in a compact metric space
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G/H is Hausdorff implies H is closed (General topology, Volume 1 by N. Bourbaki)
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Why don't we use closed covers to define compactness of metric space?
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Topology: Example of a compact set but its closure not compact
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A finite set is closed
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Show that the Hausdorff topology is unique in a finite set $X$
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Characterization of the Closure of a Set
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in a topological space only finite subsets are compact sets
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Spaces in which "$A \cap K$ is closed for all compact $K$" implies "$A$ is closed."
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Set of limit points of a subset of a Hausdorff space is closed.