What is an example of a continuous closed surjection $f : X \rightarrow Y$ from a $T_2$-space $X$ to a space $Y$ that is not $T_2$?
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@EricWofsey: Probably yes, https://math.stackexchange.com/questions/1412492/an-example-of-open-closed-continuous-image-of-t-2-space-that-is-not-t-2 does provide such an example; I have to work through all the details there. Thank you for the link; I'm surprised that my search on math.stackexchange didn't turn up that post! – murray Dec 05 '22 at 14:28
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I don't understand the argument in https://math.stackexchange.com/a/1413128/32337 that the quotient space is not $T_2$. See my comment there. – murray Dec 09 '22 at 23:38