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Question: b suppose x d is a metric space and a...

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(b) Suppose (X, d) is a metric space, and A -X with A 0. Suppose that fn : A R, and gn A R are functions for each n E N, and suppose f,g A-R are functions. Suppose fn converges to f uniformly on A and and gn converges to g uniformly on A. Suppose also that each f and gn is bounded, say |f() Kn for all E A, and Ign (x)| Mn for all E A. Prove that fngn converges uniformly to fg on A.
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