Timeline for Existence of a continuous section
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 23, 2017 at 18:51 | vote | accept | Jérémy Blanc | ||
| Nov 25, 2015 at 19:22 | comment | added | Ramiro de la Vega | You could consider $f^{-1}$ as a multivalued function from $Y$ to $X$ and then look at the various "continuous-selection-theorems" out there. For instance, if $f:[0,1] \to [0,1]$ is an open suryection and $f^{-1}(y)$ is compact for each $y$, then you have a continuous section (we don´t need to assume that $f$ is continuous or that $f^{-1}(y)$ is connected). | |
| Nov 22, 2015 at 6:32 | answer | added | Qiaochu Yuan | timeline score: 8 | |
| Nov 22, 2015 at 2:23 | answer | added | Paul Fabel | timeline score: 12 | |
| Nov 21, 2015 at 23:28 | review | Close votes | |||
| Nov 22, 2015 at 19:50 | |||||
| Nov 21, 2015 at 23:16 | comment | added | Jérémy Blanc | Thanks for the nice comment. I did not know about this result. Are there some examples where $Y=[0,1]$ ? | |
| Nov 21, 2015 at 23:12 | comment | added | Olivier Bégassat | The hairy ball theorem says that there is no section to the unit sphere bundle over the $2$-sphere : $US^2\to S^2$. | |
| Nov 21, 2015 at 23:02 | history | asked | Jérémy Blanc | CC BY-SA 3.0 |