I want to find a relation between proper map and continuous closed map $f$ where $f$ is a mapping of metric space $X$ onto a space $Y$.
Whether this is true or can be found an counterexample?
If $f$ is a continuous closed mapping of a metrizable space $X$ onto a space $Y$ then for every $y\in$ $Y$, $f^{-1}(y)$ is compact ?