I've just shown for a homework problem that if $f$ is an open continuous function from $X$ onto a $T_2$-space $Y$, and $X$ is locally compact, then $Y$ is locally compact. I wonder, does this hold for closed continuous functions too? Intuitively, I want to say no, but I'm not sure if I can find a counter example. Am I correct? How can I prove / disprove it?
2026-04-02 22:07:06.1775167626
Is local compactness preserved by continuous closed onto functions?
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