Timeline for Why should algebraic objects have naturally associated topological spaces? (Formerly: What is a topological space?)
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22 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
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| May 9, 2016 at 15:32 | comment | added | tttbase | Maybe the key point is Duality. "Now, Commutative algebra is like topology, only backwards" J Baez | |
| Aug 10, 2011 at 22:41 | answer | added | Yasha | timeline score: 3 | |
| Jun 17, 2010 at 5:03 | comment | added | Dan Ramras | Steven, unfortunately all of Grothendieck's writing has been removed from the Grothendieck circle's website. According to Wikipedia, this was requested by Grothendieck in a Jan. 2010 letter to Illusie. | |
| Feb 10, 2010 at 12:31 | history | edited | Kevin H. Lin | CC BY-SA 2.5 |
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| Feb 9, 2010 at 11:07 | answer | added | Andrew Stacey | timeline score: 13 | |
| Feb 9, 2010 at 7:49 | history | edited | Kevin H. Lin | CC BY-SA 2.5 |
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| Feb 9, 2010 at 6:43 | comment | added | Qiaochu Yuan | I think you are interpreting the phrase "put a topological structure on" too strictly. What I interpret Ilya to mean is something like "study the classifying space of a group" instead of "talking about topological groups." | |
| Feb 9, 2010 at 2:12 | answer | added | Sridhar Ramesh | timeline score: 7 | |
| Feb 9, 2010 at 0:50 | comment | added | Harry Gindi | Ilya's comment misses the entire point. This isn't a question about "topologies that are compatible with algebraic data". It's about the functorial assignment of topologies that carry algebraic data to essentially algebraic structures. | |
| Feb 9, 2010 at 0:21 | answer | added | Tom Leinster | timeline score: 17 | |
| Feb 8, 2010 at 23:47 | answer | added | François G. Dorais | timeline score: 18 | |
| Feb 8, 2010 at 22:40 | history | edited | Kevin H. Lin | CC BY-SA 2.5 |
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| Feb 8, 2010 at 21:16 | history | edited | Kevin H. Lin | CC BY-SA 2.5 |
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| Feb 8, 2010 at 19:53 | comment | added | Qiaochu Yuan | Ilya has a point; I think mathematicians like to convince themselves that what they are studying is universal but of course the priorities of human mathematicians don't remain uninfluenced by the history of their subject. | |
| Feb 8, 2010 at 18:23 | comment | added | Ilya Grigoriev | I think the fact that there are so many topological structures on various things has less to do with the things and more to do with our desire to put a topological structure on anything we study. This is the first step of trying to think of something in geometric terms rather than purely algebraically. (As various answers below explain, while the axioms are confusing at first, they try to encode quite intuitive notions of "near" and "far". The reason they are confusing is, in my opinion, that people worked hard to make these notions as general as possible, and apply them to very weird space) | |
| Feb 8, 2010 at 15:21 | answer | added | Tim Porter | timeline score: 23 | |
| Feb 8, 2010 at 13:46 | comment | added | Pete L. Clark | For what it's worth, I don't regard a functor from a category of "algebraic objects" (broadly construed) to the category Top of topological spaces as a coincidence. Is it exciting that there are highly nontrivial -- sometimes fully faithful -- functors from algebraic categories to Top? Definitely. Were the first such examples of this (by Stone) surprising to the mathematical community? Presumably (I wasn't there). But I don't like the term "coincidence" here, and I certainly did not use it myself. | |
| Feb 8, 2010 at 13:32 | comment | added | Steven Gubkin | The article is Esquisse d'un Programme (Sketch of a Program), which is available on the Grothendieck Circle website: grothendieckcircle.org The relevant part is around page 22. | |
| Feb 8, 2010 at 11:57 | comment | added | Kevin H. Lin | BTW, anyone know which Grothendieck article Allen Knutson is referring to? | |
| Feb 8, 2010 at 11:47 | answer | added | Harry Gindi | timeline score: 6 | |
| Feb 8, 2010 at 11:42 | history | asked | Kevin H. Lin | CC BY-SA 2.5 |