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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?

rossìo
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  • ok. it seems that the answer is "no": even continuity seems to be not enough, see http://math.stackexchange.com/questions/1287344/continuous-image-of-a-locally-compact-space-is-locally-compact?rq=1 – rossìo Jan 09 '17 at 14:52
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    no, every space is the continuous image of a discrete space , which are locally compact. – Henno Brandsma Jan 09 '17 at 17:48

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