Let X, Y be metric spaces and f: X->Y be a continous function on the indicated metric spaces. Prove the followings.
(a) For each subset A of X,
(b) For each subset B of Y,
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In my text, "int A" denotes the interior of A, which is the set of all interior points of A. A point x in A is an interior point of A, or A is neighborhood of x, provided that there is an open set O which contains x and is contained in A.
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