Answer for a and be should be answered independently. Let (X,d) be a metric space, and a)...

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Answer for a and be should be answered independently.

Let (X,d) be a metric space, and

a) let A ? X. Let U be the set of isolated points of A. Provethat U is relatively open in A.

b) let U and V be subsets of X. Prove that if U is both open andclosed, and V is both open and closed, then U ? V is also both openand closed.

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