2
$\begingroup$

A space is said to be KC – space if compact subsets are closed. A KC space (X,τ) is said to be Katetov – KC if there is a minimal KC – topology σ ⊆ τ. is every sequential KC - space Katetov - KC? I know that every KC space is not Katetov - KC. do you have any example to show it?

$\endgroup$
1
  • 1
    $\begingroup$ I wish there would be less of a tongue twister (mind twister)? $\endgroup$ Aug 24, 2013 at 3:00

1 Answer 1

4
$\begingroup$

It was shown in "The FDS-property and spaces in which compact sets are closed" (2004) by Alas, Tkachenko, Tkachuk and Wilson that every sequential KC-space is Katetov-KC (see Corollary 2.6).

The fact that not every KC-space is Katetov-KC was shown by Fleissner in "A $T_B$-space which is not Katetov $T_B$" (1980).

$\endgroup$
1
  • $\begingroup$ I read the whole article but I did not understand which part was exactly ma answer. $\endgroup$
    – Alireza
    Aug 6, 2013 at 18:40

Your Answer

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

Not the answer you're looking for? Browse other questions tagged or ask your own question.