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    Sequential compactness

    E-WFE4T

    Area
    Topology
    Topics
    Compactness
    Status
    draft
    • Every sequence in \(X\) has a convergent subsequence in \(X\).

    For second-countable Hausdorff spaces and metric spaces, this condition is equivalent to compactness; see E-YAEMZ.

    Solution

    The equivalence with compactness and limit-point compactness is proved in E-YAEMZ.

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