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  3. 4 a suppose xdx is a petric space a c...

Question: 4 a suppose xdx is a petric space a c...

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4.) (a) Suppose (X.dx) is a petric space. A C X. Aメ0, and f, g : A → R are uniformly continuous. If A is compact, prove that fg A R (defined by (fg)(x) -f(a)g(x) for E A) is uniformly continuous on A. Notice the difference with the previous problem. (b) Suppose A-R is a bounded, non-empty set, and f, g : A → R are uniformly continuous on A. Prove that fg is uniformly continuous on A.
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