Let $p:X\to Y$ be a closed continuous surjective map such that $p^{-1}(\{y\})$ is compact, for each $y\in Y$. (Such a map is called a perfect map) Show if $Y$ is compact, then $X$ is compact. [Hint: If $U$ is open set containing $p^{-1}(\{y\})$, there is a neighborhood $W$ of $y$ such that $p^{-...