Timeline for When does a Galois connection induce a topology?
Current License: CC BY-SA 2.5
11 events
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| Jul 19, 2017 at 17:15 | comment | added | Arpad Szaz | Clark, Your question is very good. However, the additivity of the closure operation is usually not needed. See our papers on relator spaces. Sincerely yours, Arpad Szaz | |
| Nov 7, 2013 at 2:19 | answer | added | Qiaochu Yuan | timeline score: 5 | |
| Nov 7, 2013 at 2:17 | answer | added | Qiaochu Yuan | timeline score: 5 | |
| Nov 6, 2013 at 23:40 | comment | added | Qiaochu Yuan | @Pete: the Krull topology example needs to be modified a bit, I think. The closure operator we get from the Galois correspondence doesn't send a subset of the Galois group to its closure; instead I think it sends a subset of the Galois group to the closure of the subgroup generated by it. I think this is still okay (it's a notion of closure operator internal to groups, say) but it seems worth saying. | |
| Aug 16, 2010 at 23:04 | answer | added | Nacho Lopez | timeline score: 14 | |
| Aug 16, 2010 at 9:02 | comment | added | Pete L. Clark | @Gerhard: thanks for pointing out some unfortunate typos in the definition of closure operator. (When I was typing my question, my interface with the site inexplicably became very slow, so I spent less time proofreading than usual.) Regarding Erne's book and its first chapter: I have skimmed over it and not found anything of direct relevance to my question. Please let me know if you have a specific passage in mind (the article is 138 pages). | |
| Aug 16, 2010 at 8:15 | history | edited | Pete L. Clark | CC BY-SA 2.5 |
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| Aug 16, 2010 at 7:19 | comment | added | Gerhard Paseman | Also, Marcel Erne edited a book on Galois connections, and wrote a good introductory chapter for it. I would look there first for an answer to your question. Gerhard "Ask Me About System Design" Paseman, 2010.08.16 | |
| Aug 16, 2010 at 7:16 | comment | added | Gerhard Paseman | if you have cl(x_1) contained in cl(x_2) in your C2, and cl(cl(x))=cl(x) in C3, then I would recognize it as a closure operator. Gerhard "Ask Me About System Design" Paseman, 2010.08.16 | |
| Aug 16, 2010 at 4:23 | history | edited | Pete L. Clark | CC BY-SA 2.5 |
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| Aug 16, 2010 at 4:07 | history | asked | Pete L. Clark | CC BY-SA 2.5 |