X, Y metric spaces. f:X-->Y and X is compact.(adsbygoogle = window.adsbygoogle || []).push({});

How do I prove that f is continuous if and only if G(f)={(x,f(x)):x in X} C X x Y is compact.

I think for the forward direction, since f is continuous and X is compact, then f(X) is compact. Hence, G(f)=X x f(X) is compact as a cross product of compact sets.

But for the backward direction, I am totally lost.

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# Continuity and compactness

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