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6. (12 points) Let X be a compact subset of R and let C(X) denote the set of continuous real-valued functions on X. Show that

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6. (12 points) Let X be a compact subset of R and let C(X) denote the set of continuous real-valued functions on X. Show that d(f, g) = sup{If(x) - g(2)| : I E X} defines a metric on C(X), so that C(X ) becomes a complete metric space

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