## 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.
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 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.
 Blog Entries: 8 Recognitions: Gold Member Science Advisor Staff Emeritus Try to find a counterexample. Take an nice open set in a nice space and remove a point.

## 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.
 Blog Entries: 8 Recognitions: Gold Member Science Advisor Staff Emeritus Well, what are the axioms?? Which ones are troubling you??