Timeline for closed decomposition of locally compact Hausdorff space
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 12, 2018 at 21:42 | comment | added | Douglas Somerset | This is the Arhnangelskii-Franklin paper projecteuclid.org/euclid.mmj/1029000034 | |
| Apr 12, 2018 at 18:15 | comment | added | YCor | Ah, I didn't think of the quotient, but indeed it can't be Hausdorff because it's (quasi-)compact, countable, with no isolated point. I don't know the Arhangelskii-Franklin example. I didn't even know that there could be countable spaces that are not first-countable; I haven't thought about this one. | |
| Apr 12, 2018 at 17:26 | comment | added | Douglas Somerset | The quotient space would seem to have every point a limit point and to be nowhere first countable. Is this the same as the Arhangelskii-Franklin example (which came to mind after I had posed the question)? | |
| Apr 12, 2018 at 17:06 | vote | accept | Douglas Somerset | ||
| Apr 12, 2018 at 16:48 | comment | added | YCor | Yep, homeomorphic copies of this space and partition appear in zillions of ways. | |
| Apr 12, 2018 at 16:46 | comment | added | Nate Eldredge | Equivalently, this is the ordinal $\omega^2$ with the order topology. It contains countably many limit ordinals and countably many successors, so you can partition it into sets $F_n$ containing one of each. The compactification is $\omega^2+1$. | |
| Apr 12, 2018 at 15:08 | history | answered | YCor | CC BY-SA 3.0 |