Timeline for Why the "W" in CGWH (compactly generated weakly Hausdorff spaces)?
Current License: CC BY-SA 3.0
17 events
| when toggle format | what | by | license | comment | |
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| May 24, 2023 at 23:50 | answer | added | PatrickR | timeline score: 8 | |
| Dec 11, 2015 at 4:45 | answer | added | Paul Fabel | timeline score: 10 | |
| Oct 20, 2015 at 23:17 | history | edited | David White | CC BY-SA 3.0 |
fixed typos since it was on the front page anyway
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| Oct 20, 2015 at 21:26 | answer | added | André Henriques | timeline score: 5 | |
| Oct 20, 2015 at 17:53 | comment | added | Tim Campion | It's worth mentioning the obvious: philosophically, one should expect CGWH to have nicer properties than CGH because the WH condition (diagonal is closed in the CG topology on the square) is stated in terms of the CG category, whereas the H condition (diagonal is closed in the ordinary product topology) refers back to Top, so there's a "mismatch" in the definition of CGH. It's like defining a scheme to be separated if its underlying space is Hausdorff, which is totally wrong. I would imagine that the pathologies cited in the answers here can be traced back to this mismatch. | |
| Mar 16, 2011 at 19:07 | comment | added | Mike Shulman | There are some interesting remarks in chapter 1 of May-Sigurdsson on the question of CG (there called "k-spaces") versus CGWH (there called just "CG"). | |
| Feb 16, 2011 at 17:16 | vote | accept | André Henriques | ||
| Nov 29, 2010 at 23:20 | comment | added | Todd Trimble | This is completely tangential to the question, but I feel obliged to point out some history that I've only become aware of recently: that the fundamental results on cartesian closure of CGH are not due to Steenrod but to Ronnie Brown in his 1961 thesis. The nLab page on convenient categories of topological spaces has recently been updated to include this information; for those interested, I have inserted a link to part A of Brown's thesis in the References. The nLab page is at nlab.mathforge.org/nlab/show/… Comments at the nForum are welcome. | |
| Nov 29, 2010 at 22:46 | history | edited | André Henriques | CC BY-SA 2.5 |
added 85 characters in body
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| Nov 29, 2010 at 21:57 | comment | added | David Carchedi | Well, I think what you should be asking is why use CGWH instead of CG, since after all, compactly generated spaces with no separation axiom are also Cartesian-closed etc. One thing is that compact generation for weakly Hausdorff spaces still takes the "simple form" that the space is the colimit of its compact subsets. For instance, Peter May pointed out to me that the compactly generated Grothendieck topology I introduced on CGH here: arxiv.org/abs/0907.3925 extends naturally to CGWH, but, for example, I still don't know how to extend it to CG. | |
| Nov 29, 2010 at 21:53 | answer | added | Dan Ramras | timeline score: 5 | |
| Nov 29, 2010 at 21:27 | answer | added | Charles Rezk | timeline score: 26 | |
| Nov 29, 2010 at 21:21 | answer | added | Andrey Rekalo | timeline score: 16 | |
| Nov 29, 2010 at 21:16 | comment | added | Dan Ramras | I'll offer one thought: there's an erratum to one of May's books that I seem to recall consists mainly of "adding the W." I think the issue was that colimits of Hausrorff spaces aren't always Hausdorff. The relevant erratum is on May's webpage, I think. Hopefully I'll find time to give a more directed answer, but it may be a few days. | |
| Nov 29, 2010 at 20:18 | history | edited | André Henriques | CC BY-SA 2.5 |
added 77 characters in body; edited title; added 1 characters in body
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| Nov 29, 2010 at 19:37 | comment | added | Jeff Strom | May I add to the question: to whom should the W be attributed? | |
| Nov 29, 2010 at 18:20 | history | asked | André Henriques | CC BY-SA 2.5 |