The thing is: if you have (K, d) to be a compact metric space, then how to show (C(K) , d_infinity) is complete ?( d_infinity is uniform metric)(adsbygoogle = window.adsbygoogle || []).push({});

I know maybe I should use Cauchy or triangle inequality, but I am just not clear how to construct the proof.

Anyone who has any idea about that, please help. THX!

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# How to show completeness of C(K)?

**Physics Forums | Science Articles, Homework Help, Discussion**