Timeline for Generalizing the $T_0$-axiom
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 23, 2018 at 21:43 | comment | added | Andrej Bauer | I'd just like to point out that the following definition of $T_0$ is more sensible: a space is $T_0$ if any two points that have the same neighborhoods are equal. | |
| Oct 11, 2018 at 18:06 | vote | accept | Dominic van der Zypen | ||
| Oct 11, 2018 at 18:04 | answer | added | KP Hart | timeline score: 3 | |
| Oct 11, 2018 at 17:49 | comment | added | KP Hart | I'll save you the trouble. | |
| Oct 11, 2018 at 14:01 | comment | added | KP Hart | If $\kappa$ is a limit take a cofinal set, $A$, of cardinals and have $A\cup\{\{\alpha\}:\kappa\le\alpha<\lambda\}$ as a base? | |
| Oct 11, 2018 at 13:51 | comment | added | Will Brian | Right -- thanks @KPHart. The space I defined is minimally $T^{\kappa+}_0$. It's not too hard to modify the example to find something minimally $T^\kappa_0$ as well. (I'll type out the details and post them later this morning.) | |
| Oct 11, 2018 at 13:30 | comment | added | KP Hart | @WillBrian In this way it looks like $\kappa$ itself is not split, so this is not $T^\kappa_0$. What am I missing? | |
| Oct 11, 2018 at 12:53 | comment | added | Will Brian | Can't you just take the topology on $\lambda$ with basis $\{\kappa\} \cup \{\{\alpha\} : \kappa \leq \alpha < \lambda\}$? | |
| Oct 11, 2018 at 11:54 | history | asked | Dominic van der Zypen | CC BY-SA 4.0 |