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Use this tag for questions that specifically address the role of the Hausdorff (T_2) condition, or about the set of Hausdorff topologies, etc. For a topological question with the Hausdorff assumption, just use [gn.general-topology].

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Does countable compactness imply local compactness in Hausdorff spaces?

The question arose while comparing the notions of compactness, countable compactness, local compactness, and "Lindelofness" in Hausdorff spaces. It is straightforward to show that compactness implies …