Let (fn) be a sequence of functions which is uniformly convergent on A to a limit...

 

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Let (fn) be a sequence of functions which is uniformly convergent on A to a limit function f. Let B C A and suppose fr is uniformly continuous on B for each nЄ N. Prove that f is uniformly continuous on B. Let (fn) be a sequence of functions which is uniformly convergent on A to a limit function f. Let B C A and suppose fr is uniformly continuous on B for each nЄ N. Prove that f is uniformly continuous on B.