Let (X, T ) be a topological space, (M, d) be a complete metric space and BC(X, M) := {f ∈ C(X, M); f[X] is bounded } d∞(f, g) := sup d(f(x), g(x))           (f, g ∈ BC(X, M)). Then (BC(X, M), d∞) is a complete metric space.

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