Timeline for Shape of long sequences in C(ω_1)
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 12, 2010 at 12:28 | comment | added | David R. MacIver | $\omega_1$ is normal, yes. I think all order topologies are normal aren't they? | |
| Apr 12, 2010 at 12:25 | comment | added | Sergei Ivanov | I tricked this stupid software to let me edit the post. By the way, you don't really need compactness, only normality and that every countable covering has a finite subcovering. But I don't know whether $\omega$ is normal or not. | |
| Apr 12, 2010 at 12:23 | history | edited | Sergei Ivanov | CC BY-SA 2.5 |
noted that omega1 is not compact
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| Apr 12, 2010 at 12:15 | comment | added | David R. MacIver | Hm. I was about to say that that wasn't a problem because $C(\omega_1 + 1) = C(\omega_1)$, but of course that's compact but doesn't have a countable base at every point. Vexing. | |
| Apr 12, 2010 at 12:05 | comment | added | Sergei Ivanov | For some reason, I cannot edit my answer. To clarify, it does not work for $\omega_1$: it has countable base at every point but it is not compact. | |
| Apr 12, 2010 at 9:44 | comment | added | David R. MacIver | Sorry, that sounded a bit ungrateful. Thanks for the answer! | |
| Apr 12, 2010 at 9:38 | comment | added | David R. MacIver | Believe it or not, my answer was not inspired by this, even though they are quite similar in essence. It occurred to me while I was on the train and I wrote it up before I saw this one. | |
| Apr 12, 2010 at 8:48 | history | answered | Sergei Ivanov | CC BY-SA 2.5 |