Suppose $f\colon X \rightarrow Y$ is a continuous map of topological spaces and $s\colon Y \rightarrow X$ is a continuous section to $f$, i.e., $f\circ s = 1$. If $f$ is proper does this mean that $s$ is proper as well? (A continuous map is proper if the preimage of any compact set is compact.)

This is true for schemes and I was wondering whether the same is true for topological spaces.

areseparated... – Mariano Suárez-Alvarez♦ Oct 4 '11 at 3:06