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Regular open sets ,

  1. May 24, 2012 #1
    Regular open sets,,,,

    If U is an open set in a topological space (X,τ),is it true that U=〖int〗_X 〖cl〗_X U?Justify.
     
  2. jcsd
  3. May 24, 2012 #2
    Re: Regular open sets,,,,

    please help me with this question...

    I think this says about regular open sets.
    so I need to find an open set which does not satisfy the equality given in the question above.
     
  4. May 24, 2012 #3

    micromass

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    Re: Regular open sets,,,,

    Try to find a counterexample. Take an nice open set in a nice space and remove a point.
     
  5. May 24, 2012 #4
    Re: Regular open sets,,,,

    thank you verymuch micromass.......

    I have another question regarding closure axioms.

    I know all the axioms but I'm confused with choosing two arbitrary subsets of X since it takes two possibilities for theta.

    Please somebody help me with this!!!!

    Let θ:P(X)→P(X),where θ(A)={A ;if |A| <|N|
    X ; O/W.
    Verify that θ satisfy Kuratowski closure axioms.
     
  6. May 24, 2012 #5

    micromass

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    Re: Regular open sets,,,,

    Well, what are the axioms?? Which ones are troubling you??
     
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