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# Complex Analysis watch

1. Let A and B be arbitrary subsets of R^n. Which of the following statements are true?Give a proof of the true statements and counterexamples for the false ones.

a)int (AnB) = int(A) n int(B)
b)int (AuB) = int(A) u int(B)
c)cl (AnB) =cl(A) n cl(B)
d)cl (AuB) = cl(A) u cl(B)
e)x is a limit point of A if and only if for every r>0, B(x,r) contains infinintely many points of A.
f) If A and B are open and A n B is compact, then A n B is empty.

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Updated: October 17, 2006
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