Timeline for Pontryagin dual of the surreal numbers?
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 24, 2015 at 13:43 | comment | added | Gerald Edgar | @JoelDavidHamkins: I used your comment as a basis for a new question mathoverflow.net/q/219167/454 | |
| Sep 24, 2015 at 5:48 | vote | accept | Mike Battaglia | ||
| Sep 23, 2015 at 23:25 | answer | added | Eric Wofsey | timeline score: 9 | |
| Sep 23, 2015 at 22:47 | comment | added | Todd Trimble | @GeraldEdgar I'm not sure what you mean. I don't know of any obstruction to considering the group of characters $G \to S^1$ for $G$ a topological abelian group, and such can be called the Pontryagin dual of $G$. Now for what class of topological abelian groups one has a satisfactory full duality: that's a separate question. But see this paper by Mike Barr which indicates that there are nontrivial extensions of such duality which go beyond locally compact Hausdorff abelian groups: math.mcgill.ca/barr/ftp/pdffiles/abgp.pdf | |
| Sep 23, 2015 at 22:12 | comment | added | paul garrett | As an amateur non-standard-analyst and occasional surreal-analyst ... or something ... I'd have the impression that the surreals are generally problematical by not being a set, in any case. Various incarnations of non-standard reals are sets, at least. The meaning of "finite subcover" maybe has to be non-standard-ized, or qualified by "non-standard open" or not... Probably @JoelDavidHamkins has good information at his fingertips about such. | |
| Sep 23, 2015 at 22:05 | comment | added | Joel David Hamkins | There may be set/class issues, however, since I think perhaps every set-sized open cover of a bounded interval in the surreals has a finite subcover, but there are proper class open covers with no set-sized subcover. (But I have to think more about this to be sure.) | |
| Sep 23, 2015 at 22:00 | comment | added | Gerald Edgar | For Pontryagin it must be locally compact. If you do not mean the discrete topology, what do you mean by "suitably topologized"? | |
| Sep 23, 2015 at 22:00 | comment | added | Joel David Hamkins | Unless I am mistaken, it seems to me that the surreals in the order topology are not locally compact. Does this cause a problem? | |
| Sep 23, 2015 at 21:49 | history | asked | Mike Battaglia | CC BY-SA 3.0 |