4. Let D be a subset of R. (a) A point xo in D is said to be an isolated point of D provided that there is an r > 0 such that the only point of D in the interval (xor, xo + r) is xo itself. Prove that a point xo in D is either an isolated point of D or an limit point of D. (b) Let f Z→ R be a function defined on the set of integers Z. When will f be a continuous function? Find some example that f is continuous or discontinuous. Justify your answer.

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