3
$\begingroup$

A space X is countably compactly generated if it can be written as countable direct limit of compact Hausdorff spaces.

Are countably compactly generated spaces paracompact spaces? Do we have partition of unity for countably compactly generated spaces?

$\endgroup$
3
  • $\begingroup$ Are you assuming that the compact Hausdorff spaces that enter the colimit are themselves separable, or even second countable? $\endgroup$ Dec 2, 2014 at 16:43
  • 2
    $\begingroup$ Asked already: math.stackexchange.com/q/1047888/94514 $\endgroup$ Dec 2, 2014 at 16:45
  • $\begingroup$ If the final space is regular, the answer is yes: a countably compactly generated space is Lindelöf (or I am missing something ?), and a Lindelöf regular space is paracompact. $\endgroup$ Dec 3, 2014 at 8:47

0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.