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Question: suppose fn converges uniformly to f on the compact interval...

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Suppose fn converges uniformly to f on the compact interval [a, b] Suppose gn is a sequence of function converging uniformly to g on [a, b]. Suppose further that f: [c, d] - [a, b] is a continuous function. Is it true that f: [c, d] - [a, b] Is it true that g f converges uniformly to g o f on [c, d]?

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