Let $\displaystyle X$ and $\displaystyle Y$be topological spaces with $\displaystyle Y$compact and let $\displaystyle p_X : X \times Y \rightarrow X$denote the projection of the topological product on $\displaystyle X$, $\displaystyle p_X (x,y) = x$.Given that $\displaystyle W \subseteq X \times Y$is closed in $\displaystyle X \times Y$, prove that $\displaystyle p_X (W)$ is closed inX.