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SOLVED: Problem 4 Show that a set A is compact if and only if every infinite subset has an accumulation point in A.
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Gabriel Peyré on Twitter: "The space of compact sets in a metric space is a compact set for the Hausdorff metric. Hausdorff convergence is weak and does not preserve topology, dimension, length
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Closed subset of a compact set is compact | Compact set | Real analysis | Topology | Compactness - YouTube