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Characterization of Relative Compactness in Complete Metric Spaces
Let $(M, d)$ be a complete metric space and $A\subseteq M$. I want to show that $A$ is relatively compact (i.e., $\overline A$ is compact) iff there exists no infinite subset $S\subseteq A$ such that...
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I would give a very different proof using the following standard characterization of relative compactness: A subset of a complete metric space is relatively compact if and only if it is totally...
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