Timeline for Relatively countably compact subsets without countably compact closure.
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
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| Nov 12, 2023 at 15:52 | comment | added | Pietro Majer | (one may also say that A is even sequentially compact, because it is the product of two seq. comp. topological spaces) | |
| Jul 8, 2010 at 9:42 | comment | added | KP Hart | You may want to replace `non-normal' by normal in the first line. | |
| Jul 6, 2010 at 14:30 | comment | added | Henno Brandsma | Adde: we cannot have a countably compact $A$ with non-countably compact closure for a non-normal space, like here, because cl(A) would then be pseudocompact (having a dense countably compact subset) and hence (by normality) countably compact. But, can we still have a relatively countably compact $A$ in a $T_4$ space $X$ with non countably compact closure? | |
| Jul 6, 2010 at 4:29 | comment | added | Henno Brandsma | Ah, the Tychonoff plank. I tried to define a similar example on $\omega \times \omega$, but failed... Is it essential that such a space be non-normal, as this is? | |
| Jul 6, 2010 at 4:26 | vote | accept | Henno Brandsma | ||
| Jul 6, 2010 at 1:38 | history | edited | Joel David Hamkins | CC BY-SA 2.5 |
Improved presentation. Added crude diagram.
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| Jul 6, 2010 at 0:29 | history | answered | Joel David Hamkins | CC BY-SA 2.5 |