Let f be a sequence of continuous, real valued functions on [0, 1] which converges uniformly...
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Let f be a sequence of continuous, real valued functions on [0, 1] which converges uniformly to f. Prove that limn→x fn(n) = f(1/2) for any sequence {n} which converges to 1/2. (b) Must the conclusion still hold if the convergence is only point-wise? Explain. Let f be a sequence of continuous, real valued functions on [0, 1] which converges uniformly to f. Prove that limn→x fn(n) = f(1/2) for any sequence {n} which converges to 1/2. (b) Must the conclusion still hold if the convergence is only point-wise? Explain.
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Related Book For
Introduction to Real Analysis
ISBN: 978-0471433316
4th edition
Authors: Robert G. Bartle, Donald R. Sherbert
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