Timeline for A generalized diagonal?
Current License: CC BY-SA 3.0
2 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 3, 2015 at 13:59 | comment | added | Vladimir Tkachev | Thank you for good examples! Probably it should be made more precise what kind of $X$ and $ f$ are relevant. I've also considered a similar cubic polynomial, but with the domain of definition being the whole $ X =\mathbb {R} $ instead of an interval. In that case, $ E (f)$ is connected (being the union of an oval and a diagonal line passing through the oval). The example you construct can be thought as a cutoff of the set $E(f)$ above. Thus, some 'completteness' of X is needed. Another relevant example is $ f=\sin x\sin y:\,\mathbb {R}^2\to\mathbb {R}$ for which $ E(f) $ is connected again. | |
| Jan 1, 2015 at 23:14 | history | answered | Włodzimierz Holsztyński | CC BY-SA 3.0 |