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    Is R Compact with This Topology?

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    Please solve the following problem:

    " Let X be any set with infinite elements ; is it true that
    A = { A a subset of X : X - A is either finite or countable} U { X,0} is a topology on X ?. Why ? ( note: the 0 means the empty set).

    Is R compact with this topology?

    © BrainMass Inc. brainmass.com October 10, 2019, 2:31 am ad1c9bdddf
    https://brainmass.com/math/geometry-and-topology/compact-topology-381096

    Solution Summary

    The solution determines if R is compact with the topology.

    $2.19