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Question about interior.

  1. Sep 18, 2012 #1
    If I have the statement Cl(X-A)=X-Int(A)
    X and A are topological spaces. Does this statement work in infinite dimensions and uncountable dimensions. I think it would just wondering.
     
  2. jcsd
  3. Sep 18, 2012 #2
    What do you mean with "dimension" in topology in the first place?

    But yes, the statement is always true as you can easily check for yourself.
     
  4. Sep 18, 2012 #3

    HallsofIvy

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    Science Advisor

    Most topological spaces do define "dimension". Nor does it make sense to talk about X and A both being topologica spaces. I think you mean X is a topological space and A is a subset of X. But it is true that in any topological space that the closure of X- A is X- the interior of A.
     
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