If A and B are subsets of a metric space (X,d), show that int(A∩B) = int(A)∩int(B). Find an example where int(A∪B)≠int(A)∪int(B)
I've done the second part of the question, but could anyone help me to do the first part of the question?
LET int( , then there exists a δ>0 and such that:
BUT from set theory we have that for any S,T,R SETS :
AND according to that:
.................................................. ..........................................2
hence int(A) int(B)
For the converse use again (1) identity