I know this theorem and its proof, my question is that, what is the name of this theorem? Some guys refers it as "Hausdorff theorem", but I am not sure.
2026-03-30 05:13:45.1774847625
Name of the theorem "any totally bounded and closed subset in a complete metric space, is compact"
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I'm not sure this has any simple name; Paul Sally's book calls it the Heine-Borel Theorem, but most sources name Heine-Borel a much more specific specialization of this broad result.