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Closed set in a compact set

  1. Dec 10, 2007 #1
    1. The problem statement, all variables and given/known data
    Let X be a topological space. Let A be compact in X. Let B be contained in A. Let B also be closed in X. Is it always true that B is compact in X?


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Dec 10, 2007 #2

    morphism

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    B will be compact in A, and consequently in X as well.
     
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