Continuous function on metric spaces.

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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