Problems and Solutions in EAL AND COMPLEX ANALYSIS
1 REAL ANALYSIS 1 Real Analysis 1.1 1991 November 21 1.(a) Let f nbe a sequence of continuous, real valued functions on [0;1] which converges uniformly to f.Prove that lim n!1f n(x n) = f(1=2) for any sequence fx ngwhich converges to 1=2. (b) Must the conclusion still hold if the convergence is only point-wise?
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