Timeline for What is a reference for profinite sets?
Current License: CC BY-SA 2.5
21 events
| when toggle format | what | by | license | comment | |
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| Jun 27, 2011 at 3:20 | comment | added | Yemon Choi | without wishing to disturb settled matters: one data point not mentioned here is that the primitive ideal spaces of C*-algebras can give natural and nontrivial non-Hausdorff compact spaces. (That said, people who work with them sometimes say they are quasicompact.) | |
| Mar 3, 2010 at 19:48 | comment | added | Leonid Positselski | Since you still haven't taken care to substantiate either of these claims, I don't see anything to discuss here. | |
| Mar 3, 2010 at 18:51 | comment | added | Harry Gindi | Compact non-Hausdorff spaces are important, though perhaps not in your specific field. As I was saying, "compact presumes Hausdorff" is not conventional enough to use it without note, whence Tom's remark. | |
| Mar 3, 2010 at 17:50 | comment | added | Leonid Positselski | I did not say non-Hausdorff topological spaces are not important, I said non-Hausdorff compact topological spaces are not important, except in the context of Zariski topology. The terminology "compact presumes Hausdorff" is at least as conventional as the terminology "compact does not presume Hausdorff", which is a quite sufficient justification for me using it here. | |
| Mar 3, 2010 at 17:20 | comment | added | Harry Gindi | @Leonid: Non-Hausdorff topological spaces are not important in what sense? That's not really true at all. Also, that compact means "qc+Hausdorff" has not been standard for a while. Something like a generation (or more) of people have been taught that compact means "every open cover contains a finite subcover". That is what Prof. Leinster meant by "Unless you're being a bit merciless with your terminology". | |
| Mar 3, 2010 at 16:04 | comment | added | Leonid Positselski | @fpqc: It is just because non-Hausdorff compact topological spaces are not very useful or interesting in my view, if one is not dealing with schemes and Zariski topology. So it makes sense to use the shortest term for the most useable concept. And it seems to me that "compact" presuming Hausdorff is the standard terminology in general topology. | |
| Mar 3, 2010 at 14:13 | comment | added | Harry Gindi | @Leonid: Only algebraic geometers make that distinction. Do you say quasilocal for "has a unique maximal ideal" and local for "quasilocal + noetherian" like a commutative algebraist? I don't understand why AG people like to make it an issue. We realize that all of the standard texts use "quasicompact", but I doubt that using "quasicompact" instead of "compact" is ever going to catch on outside of AG. Also, it's silly because Hausdorff spaces pretty much never come up in AG. | |
| Mar 3, 2010 at 10:51 | comment | added | Leonid Positselski | @Tom: In the terminology I am used to, "compact" presumes Hausdorff (when it doesn't, the term "quasicompact" is being used). | |
| Mar 3, 2010 at 4:23 | comment | added | Harry Gindi | I'm also not familiar with twitter, having never used it. | |
| Mar 3, 2010 at 3:22 | comment | added | Harry Gindi | @Reid: I was giving another name. I didn't think it would be too hard to look up. | |
| Mar 3, 2010 at 0:58 | comment | added | Tom Leinster | Leonid, you either forgot "Hausdorff" or you were being a bit merciless with your terminology :-) Also: another name for profinite spaces is Stone spaces. | |
| Mar 2, 2010 at 23:54 | vote | accept | jackie boy | ||
| Mar 2, 2010 at 23:54 | vote | accept | jackie boy | ||
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| Mar 2, 2010 at 23:53 | vote | accept | jackie boy | ||
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| Mar 2, 2010 at 22:54 | vote | accept | jackie boy | ||
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| Mar 2, 2010 at 22:44 | comment | added | Reid Barton | @fpqc: this is not Twitter. If you have something to say, please use whole sentences, and explain how your comment is relevant (are you pointing out an error in Leonid's answer? giving an alternate description? etc.) | |
| Mar 2, 2010 at 22:39 | comment | added | Marty | An $\ell$-space is the terminology used by Bernstein for a locally compact, totally disconnected, Hausdorff (maybe this last adjective is redundant) topological space. It seems that fpqc has been reading up on $p$-adic groups lately - I'll have to talk to DeBacker about this! ;) | |
| Mar 2, 2010 at 22:38 | history | edited | Leonid Positselski | CC BY-SA 2.5 |
corrected spelling
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| Mar 2, 2010 at 22:09 | comment | added | Leonid Positselski | What's an \ell-space? | |
| Mar 2, 2010 at 21:57 | comment | added | Harry Gindi | Compact $\ell$-space. | |
| Mar 2, 2010 at 21:54 | history | answered | Leonid Positselski | CC BY-SA 2.5 |