2002-70.md

course	course_year	question_number	tags	title	year
Further Analysis	IB	70	IB 2002 Further Analysis	3.I.3G	2002

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

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

(a) Show that if $Y$ is Hausdorff, then $G_{f}$ is closed in $X \times Y$.

(b) Show that if $X$ is compact, then $G_{f}$ is also compact.