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Math Help - Topology Question

  1. #1
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    Topology Question

    Question 1

    (a) Give an example of a space where the discrete topology is the same as the finite complement topology.
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  2. #2
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    Quote Originally Posted by flaming View Post
    Question 1

    (a) Give an example of a space where the discrete topology is the same as the finite complement topology.
    Let X be a finite set. Then the discrete topology is simply \mathcal{P}(X). But since X is finite it means the complement of any Y\subseteq X is finite. Thus, the finite complement topology consists of all subsets of X i.e. \mathcal{P}(X).
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