Open Sets in Topological Spaces: Understanding U=intcl U

[99butterfly]

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.

 

[99butterfly]

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.

 

[micromass]

Try to find a counterexample. Take an nice open set in a nice space and remove a point.

 

[99butterfly]

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.

 

[micromass]

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