Question: I really need some help with this problem. Let (X, p) be a compact metric space and consider the space of continuous real functions C

I really need some help with this problem.

Let (X, p) be a compact metric space and consider the space of continuous real functions C (X). Prove that the distance d(f,g) := sup |f(~'c) 9(w)l 16X is indeed a metric on C (X) Show also that this space is complete. Hint: Be very explicite showing that your Cauchy sequence converges to an appropriately chosen limiting function

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