3. Suppose that (X, d) is a metric space which is not compact. Let {an}_1 be a sequence of distinct points in X that has no convergent subsequences. For each nЄ N, take rn > 0 such that Brn (an)Brm (am) = 0 for n‡m. Let and fn(2): := rn - d(x, a) ™n +d(x, an) n I fn(x), if x € Brn (an) for some n € N; otherwise. f(x) = { 0, Show that fn and f are continuous functions. Is f bounded?

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