Further Analysis | Part IB, 2002

Let f:XYf: X \rightarrow Y be a continuous map between topological spaces. Let

Gf={(x,f(x)):xX}.G_{f}=\{(x, f(x)): x \in X\} .

(a) Show that if YY is Hausdorff, then GfG_{f} is closed in X×YX \times Y.

(b) Show that if XX is compact, then GfG_{f} is also compact.

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