Timeline for Compact and quasi-compact
Current License: CC BY-SA 2.5
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 18, 2010 at 4:11 | vote | accept | Harry Gindi | ||
| Mar 4, 2010 at 1:09 | comment | added | Pete L. Clark | By the way, I attended an excellent algebraic geometry seminar talk today: it was about various "compactifications" of various moduli spaces. I resisted the temptation to point out that they were already quasi-compact. (P.S.: yes, I am not that far from being an algebraic geometer, if that was not already clear. Lots of mathematicians in adjacent fields would say the same.) | |
| Mar 3, 2010 at 21:27 | comment | added | JBorger | It would be nice if "analytically compact" and "algebraically compact" became standard. | |
| Mar 3, 2010 at 18:43 | comment | added | Pete L. Clark | @Gerald: if we're talking serious standard references, yes, I believe this is correct. But the list of serious standard references for GT is very short: I would include also Willard and Kelley. I would say Munkres' book is an excellent undergraduate text. Note by the way that the latest edition of Engelking's book has 706 citations on MathSciNet -- it is indubitably a standard reference. (Kelley: 112. Willard: 139 total from the last two editions. Munkres: 156.) | |
| Mar 3, 2010 at 18:10 | comment | added | Gerald Edgar | @Pete: I found your remark surprising. Some googling led to a page with this on it: Bourbaki and Engelking [Bou66, Eng89] use the term "quasi-compact" instead, suggesting that all other topology textbooks use "compact" and "compact Hausdorff". | |
| Mar 3, 2010 at 18:00 | comment | added | Harry Gindi | Alright, thanks. That's good to know. I was under the impression that the convention was much more one-sided, as per Mariano's remark. | |
| Mar 3, 2010 at 17:48 | comment | added | Pete L. Clark | It really is a standard convention in mathematics. For instance, one of the standard references for the subject of its title is Ryszard Engelking's General Topology (latest edition published 1989). In Engelking's text, compact implies Hausdorff. And so forth. To ardently campaign for one position or the other is, in my view, just advertising which texts you haven't read. When writing about compact spaces, it is important to make clear what "compact" means. Either usage, without any explanation, will be confusing to some people. | |
| Mar 3, 2010 at 17:11 | comment | added | Harry Gindi | Prof. Clark, a comment on your comment in Prof. Conrad's answer: While you may use compact to mean qc+Hausdorff in your field (arithmetic geometry, right?), it seems pointless to carry this convention over to papers in fields where it is nonstandard, since it is needlessly confusing with very few benefits. | |
| Mar 3, 2010 at 16:26 | history | edited | Pete L. Clark | CC BY-SA 2.5 |
added 794 characters in body; deleted 3 characters in body
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| Mar 3, 2010 at 16:12 | history | answered | Pete L. Clark | CC BY-SA 2.5 |