Timeline for Are definable sets in an o-minimal expansion of the real field locally analytic?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 26, 2016 at 22:53 | vote | accept | Dima Sustretov | ||
| Mar 26, 2016 at 22:53 | comment | added | Dima Sustretov | Dear @ACL, thank you for your answer, which comes as a surprise for me: I really expected that the setting of o-minimality forces definable sets to be "nice", but as it turns out, analyticity is not a part of the "niceness". | |
| Mar 23, 2016 at 17:36 | comment | added | Todd Trimble | @EmilJeřábek Ah, thank you. Just to go straight to the source: Olivier Le Gal and Jean-Philippe Rolin, An o-minimal structure which does not admit $C^\infty$ cellular decomposition, Ann. Inst. Fourier (Grenoble), 59 (2009), pp. 543–562. | |
| Mar 23, 2016 at 17:29 | comment | added | ACL | @EmilJeřábek : I would guess that every function in this structure is piecewise locally analytic. | |
| Mar 23, 2016 at 17:25 | comment | added | Emil Jeřábek | @ACL: Do you happen to know anything about the follow-up question mentioned in the comments, that is, when the o-minimal structure is an expansion of the real field only by locally analytic functions? | |
| Mar 23, 2016 at 17:23 | comment | added | Emil Jeřábek | @ToddTrimble: The answer is also no. See my last comment below the question. | |
| Mar 23, 2016 at 17:22 | comment | added | Todd Trimble | I guess the situation is still unknown if we replace the word "analytic" by "$C^\infty$"? | |
| Mar 23, 2016 at 17:15 | history | answered | ACL | CC BY-SA 3.0 |