Let $f:M\to N$ be a continuous and proper map.
Let $a$ be in $\operatorname{Range}(f)$, and $f^{-1}(a)$ contained in a nbhd $U$.
Why is there a nbhd $W$ of $a$ s.t. $f^{-1}(W)$ is contained in U?
Let $f:M\to N$ be a continuous and proper map.
Let $a$ be in $\operatorname{Range}(f)$, and $f^{-1}(a)$ contained in a nbhd $U$.
Why is there a nbhd $W$ of $a$ s.t. $f^{-1}(W)$ is contained in U?