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    Compactness and limit-point compactness

    E-E7FYR

    Area
    Topology
    Topics
    Compactness
    Status
    draft

    • \(X\) is compact

    • Every infinite subset \(A\subseteq X\) has a limit point in \(X\).

    The conditions are equivalent when \(X\) is second countable and Hausdorff, or metrizable; see E-YAEMZ.

    Solution

    The proof is given in E-YAEMZ, together with the equivalence to sequential compactness.

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