Suppose (fn) is a sequence of continuous functions on an interval I that converges uniformly on I

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Suppose (fn) is a sequence of continuous functions on an interval I that converges uniformly on I to a function f. If (xn) ⊂ I converges to x0 ∈ I, show that lim(fn(xn)) = f (x0).
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Introduction to Real Analysis

ISBN: 978-0471433316

4th edition

Authors: Robert G. Bartle, Donald R. Sherbert

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