Hi i'm using Kreyszig's Introductory Functional Analysis with Applications and he proves that the set of continuous functions on an interval [a,b] under the metric d(x,y) = max|x(t)-y(t)| is complete. Standard proof nothing hard over there.(adsbygoogle = window.adsbygoogle || []).push({});

But isn't the sequence of x^n s on [0,1] a Cauchy sequence (under this metric) which does Not converge to a continuous function?

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# Function Space C[a,b]

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