Timeline for Possible categorical reformulation for the usual definition of compactness
Current License: CC BY-SA 3.0
20 events
| when toggle format | what | by | license | comment | |
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| Nov 26, 2019 at 8:40 | comment | added | Andrej Bauer | A useful point of view is that the open subsets of $X$ are in bijective correspondence with continuous maps $X \to \Sigma$ where $\Sigma$ is the Sierpinski space. Compactness can be expressed in terms of such maps. | |
| Mar 10, 2015 at 1:47 | comment | added | Oleg Viro | Dear Qiaochu Yuan, thanks for the reference to ncatlab. Unfortunately, they failed to deal with the true compactness of topological spaces. | |
| Mar 9, 2015 at 12:30 | comment | added | user13113 | You may find the notion of a Grothendieck topology interesting. | |
| Mar 9, 2015 at 11:06 | answer | added | Paul Taylor | timeline score: 0 | |
| Mar 9, 2015 at 5:59 | comment | added | Qiaochu Yuan | Regarding the edit, perhaps ncatlab.org/nlab/show/compact+object might be helpful. | |
| Mar 9, 2015 at 5:42 | vote | accept | Oleg Viro | ||
| Mar 9, 2015 at 5:42 | vote | accept | Oleg Viro | ||
| Mar 9, 2015 at 5:42 | |||||
| Mar 9, 2015 at 5:41 | history | edited | Oleg Viro | CC BY-SA 3.0 |
added 454 characters in body
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| Mar 9, 2015 at 5:13 | vote | accept | Oleg Viro | ||
| Mar 9, 2015 at 5:42 | |||||
| Mar 9, 2015 at 5:13 | vote | accept | Oleg Viro | ||
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| Mar 9, 2015 at 5:09 | vote | accept | Oleg Viro | ||
| Mar 9, 2015 at 5:13 | |||||
| Mar 9, 2015 at 5:05 | vote | accept | Oleg Viro | ||
| Mar 9, 2015 at 5:07 | |||||
| Mar 9, 2015 at 5:04 | vote | accept | Oleg Viro | ||
| Mar 9, 2015 at 5:05 | |||||
| Mar 9, 2015 at 5:03 | vote | accept | Oleg Viro | ||
| Mar 9, 2015 at 5:04 | |||||
| Mar 9, 2015 at 3:53 | comment | added | Eric Wofsey | You want to require that the images of the $f_i$ cover $X$; otherwise any discrete space has this property (you can always just take the empty subfamily). | |
| Mar 9, 2015 at 3:39 | answer | added | Eric Wofsey | timeline score: 18 | |
| Mar 9, 2015 at 2:59 | answer | added | Dave Witte Morris | timeline score: 14 | |
| Mar 8, 2015 at 22:17 | comment | added | Todd Trimble | Welcome to MathOverflow, Professor Viro. | |
| Mar 8, 2015 at 21:28 | review | First posts | |||
| Mar 8, 2015 at 21:38 | |||||
| Mar 8, 2015 at 21:26 | history | asked | Oleg Viro | CC BY-SA 3.0 |