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    Compact and perfect sets

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    If P is a perfect set and K is compact is the intersection P intersection K always compact?always perfect?.

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    https://brainmass.com/math/geometry-and-topology/compact-and-perfect-sets-27184

    Solution Preview

    Proof:

    P is perfect if and only P=P', where P' is the set of limit points of P. K is compact. Let Q=P intersects K

    1. Q is also compact.
    ...

    Solution Summary

    If P is a perfect set and K is compact is the intersection P intersection K always compact?always perfect?.

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