Let X be a set, and let f(adsbygoogle = window.adsbygoogle || []).push({}); _{n}: X [tex]\rightarrow[/tex] R be a sequence of functions. Let p be the uniform metric on the space R^{x}. Show that the sequence (f_{n}) converges uniformly to the function f : X [tex]\rightarrow[/tex] R if and only if the sequence (f_{n}) converges to f as elements of the metric space

(R^{X}, p)

I'm not sure how to do this problem...

Can someone help me out?

Thanks!

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# Metric Spaces

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