Let $X$ be a locally compact Hausdorff space, $Y$ a Hausdorff space and
$f : X \to Y$
a Borel map. Is $f(Y)$ locally compact?
Let $X$ be a locally compact Hausdorff space, $Y$ a Hausdorff space and
$f : X \to Y$
a Borel map. Is $f(Y)$ locally compact?