Timeline for The continuous as the limit of the discrete
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 7, 2010 at 22:45 | comment | added | Pete L. Clark | When thinking in terms of topologies on groups, you have to be careful. If one were not "gunning for the circle", it would seem natural -- and is certainly the correct thing to do in many instances -- to put the direct limit topology on $\mathbb{Q}/\mathbb{Z}$, i.e., the discrete topology. This makes it into a complete topological group, so it is certainly not dense in some other topological group like the circle. I think that Tao's remark is rather vague (there is no such thing as a "continuous space"), but M. Emerton is probably on the right track in his Gromov-Hausdorff response. | |
| Feb 7, 2010 at 21:47 | comment | added | user717 | Okay, then I can also remove my comment :) | |
| Feb 7, 2010 at 20:54 | history | edited | Qiaochu Yuan | CC BY-SA 2.5 |
added 716 characters in body
|
| Feb 7, 2010 at 20:47 | comment | added | Harry Gindi | My mistake. I've given you a +1 to compensate for my incorrectness. | |
| Feb 7, 2010 at 20:40 | comment | added | Qiaochu Yuan | Harry, you are the only person in this discussion who's brought up the profinite integers. What makes you think the OP is asking a question about the profinite integers? | |
| Feb 7, 2010 at 20:26 | history | edited | Qiaochu Yuan | CC BY-SA 2.5 |
added 394 characters in body
|
| Feb 7, 2010 at 20:18 | history | answered | Qiaochu Yuan | CC BY-SA 2.5 |