in Mathematics, 39 mins ago, by
user193319 Problem: Let $X$ be some locally compact space, $Y$ some generic topological space, and $f : X \to Y$ a continuous open map. Show that $f(X)$ is locally compact. Here is my proof: Let $y \in f(X)$. Then there exists an $x \in X$ such that $f(x) = y$. Since $X$ is locally compact, there exists $C \in X$ compact such that $x \in U \subseteq C$, where $U$ is some open nbhd of $x$. Then $y = f(x) \in f(U) \subseteq f(C)$. Since $f$ is open, $f(U)$ will be open;