Answer to Question #170331 in Real Analysis for Prathibha Rose

Question

Consider the metric space (B(s),d) of all bounded real valued functions on a non empty set S , with metric d(f,g) =||f-g|| ,where ||f|| =sup _{x element of s}{|f(x)|} prove that f_n converges to f in the metric space (B(s),d) if and only if f_n converges to f uniformly on S

Answer 1

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