Skip to main content
MathOverflow

Return to Answer

Thanks to Eric Wofsey, we have added the necessary extra hypothesis that Y is compactly generated.
Source Link
Paul Fabel
Paul Fabel
  • 2k
  • 15
  • 23

Yes. Let Y be any compactly generated connected Hausdorff space such that Y fails to be locally compact. Let X be the one point compactification. X is maximal compact (since compact subsets of X are closed), but X is not Hausdorff.

See for example, Example 99 from Counterexamples in Topology by Steen and Seebach.

Yes. Let Y be any connected Hausdorff space such that Y fails to be locally compact. Let X be the one point compactification. X is maximal compact (since compact subsets of X are closed), but X is not Hausdorff.

See for example, Example 99 from Counterexamples in Topology by Steen and Seebach.

Yes. Let Y be any compactly generated connected Hausdorff space such that Y fails to be locally compact. Let X be the one point compactification. X is maximal compact (since compact subsets of X are closed), but X is not Hausdorff.

See for example, Example 99 from Counterexamples in Topology by Steen and Seebach.

Source Link
Paul Fabel
Paul Fabel
  • 2k
  • 15
  • 23

Yes. Let Y be any connected Hausdorff space such that Y fails to be locally compact. Let X be the one point compactification. X is maximal compact (since compact subsets of X are closed), but X is not Hausdorff.

See for example, Example 99 from Counterexamples in Topology by Steen and Seebach.