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Closure question

  1. Nov 12, 2008 #1
    Prove or disprove

    Closure of the Interior of a closed set X is equal to X
    so clos(intX)=X

    I think it is true, but i don't know how to prove it

    I thought that clos(int(X))=int(X)+bdy(int(X))=X


  2. jcsd
  3. Nov 12, 2008 #2


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    Science Advisor

    Think carefully. Consider the singleton set {p} containing only the single point p. In any metric topology, such a set is closed. What is its interior? What is the closure of that interior.
  4. Nov 12, 2008 #3
    What if the interior is non-empty?
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