I'm stuck on this statement. Could anyone please help me out?
Let $X$ be a compact manifold, every map $f: X \longrightarrow Y$ is proper.
The definition of proper: a smooth map between manifolds is called proper if inverse images of compact subsets are compact.
I know that continuous maps map compact sets to compact sets. But this seems to be the converse of that... Is there anything that I'm missing here? Thanks!