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Apr 17, 2015 at 14:00 history edited Paul Fabel CC BY-SA 3.0
Thanks to Eric Wofsey, we have added the necessary extra hypothesis that Y is compactly generated.
Apr 17, 2015 at 9:14 comment added Eric Wofsey The one-point compactification will not be maximal compact unless $Y$ is compactly generated. Indeed, if $A\subset Y$ has closed intersection with every compact set but is not closed, then $A\cap \{\infty\}$ is compact but not closed in the one-point compactification.
Apr 17, 2015 at 8:46 vote accept Dominic van der Zypen
Apr 18, 2015 at 13:02
Apr 17, 2015 at 8:30 history answered Paul Fabel CC BY-SA 3.0