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Oct23-08, 01:28 PM
P: 1,367
Maybe for you but no for me: Let A', B' be the complements of A, B in E. Then B' is a subset of A' since A is a subset of B. Pick a p in A'. If p is in B', then we can find an open ball centered at p entirely contained in B' and consequently in A'. But what if p is not in B', i.e. what if p is in B?