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A bounded function

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(X,d) set of all bounded functions on X
prove that (B(X), is a metric space
B(X) is the h) is complete where h is the metric h(f,g) = sup{If(x)-g(x)I, x in X}

Edit If(x)-g(x)I means the absolute value of f(x)-g(x)

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Solution Summary

A bounded function is defined here.

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