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I have a proof that I need to try to work out but I'm not really getting too far and need help if you could at all. The question is

Let A and B be two subsets of a metric space X. Prove that:

Int(A)[tex]\bigcup[/tex]Int(B)[tex]\subseteq[/tex]Int(A[tex]\bigcup[/tex]B)andInt(A)[tex]\bigcap[/tex]Int(B) = Int(A[tex]\bigcap[/tex]B)

I also have to give an example of two subsets A and B such that Int(A) [tex]\bigcup[/tex] Int (B) ≠ Int (A[tex]\bigcup[/tex] B)

Any help at all would be so great

Cheers

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# Help with a topology proof

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