Problem 7 (16 points). Let fn be a sequence of continuous functions on a closed interval [a, b] such that fn pointwise converges to a bounded function f on [a, b]. (a) Is it necessary that the convergence of fan to f is uniform? Give a positive proof or a counterexample. (b) Would your answer to part (a) be different if we additionally assume that f is continuous on [a, b]? Justify your answer
