Timeline for The continuous as the limit of the discrete
Current License: CC BY-SA 2.5
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 7, 2010 at 23:48 | comment | added | Pete L. Clark | Has anyone considered asking Terry Tao what he meant? He's a MOer and very responsive to questions. | |
| Feb 7, 2010 at 23:04 | comment | added | S. Carnahan♦ | I'd like to comment on the quote. The cyclic groups in the sequence are not given with a chain of homomorphisms into each other, so this suggests the author already had a system of embeddings into some topological target space in mind (e.g., (1/n)Z/Z into R/Z or roots of unity into the complex unit circle). | |
| Feb 7, 2010 at 21:33 | comment | added | Gian Maria Dall'Ara | Sorry I realized only after writing that QY gives substantially an answer to my question in his discussion below. | |
| Feb 7, 2010 at 21:29 | comment | added | Gian Maria Dall'Ara | I was thinking about the system of cyclic groups and morphisms given by non trivial maps from Z_m to Z_n only when m divides n. I was wondering whether there is a natural category of topological groups where the circle is the inductive (or direct) limit of such a system. | |
| Feb 7, 2010 at 21:12 | comment | added | Qiaochu Yuan | I guess it's also worth pointing out that "limit" as Tao is using it is not quite the same as "limit" in the category-theoretic sense, which is the sense several of us have been using. | |
| Feb 7, 2010 at 20:55 | answer | added | Emerton | timeline score: 2 | |
| Feb 7, 2010 at 20:26 | comment | added | Harry Gindi | Or even better, projective and inductive. The way I keep them all straight is by remembering that pushouts are colimits, since they push out to the bottom right, so they're left=>right is direct. right=>left =inverse limit = limit. | |
| Feb 7, 2010 at 20:18 | answer | added | Qiaochu Yuan | timeline score: 6 | |
| Feb 7, 2010 at 18:55 | comment | added | Pete L. Clark | @QY: In many areas of mathematics, including algebra, one says "direct limit" and "inverse limit" -- not "colimit" and "limit" -- for this type of construction. | |
| Feb 7, 2010 at 16:33 | comment | added | Qiaochu Yuan | Q/Z is a colimit, not a limit, of the finite cyclic groups. | |
| Feb 7, 2010 at 16:01 | answer | added | Harald Hanche-Olsen | timeline score: 5 | |
| Feb 7, 2010 at 14:02 | comment | added | Gian Maria Dall'Ara | Is it possible that the circle can be viewed as the inductive limit of the ciclic groups in some appropriate category of topological groups? | |
| Feb 7, 2010 at 12:10 | history | asked | Matt | CC BY-SA 2.5 |