Timeline for Topological Content of the Kakutani Fixed Point Theorem
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 3, 2017 at 15:41 | answer | added | Pete Caradonna | timeline score: 3 | |
| Jul 2, 2013 at 11:26 | comment | added | Michael Greinecker | @TorstenEkedahl No, you can't. The Michael selection theorem requires the correspondence to be lower hemicontinuous, not upper hemicontinuous. | |
| Dec 6, 2010 at 22:23 | answer | added | Chris Heunen | timeline score: 2 | |
| Apr 25, 2010 at 7:37 | answer | added | Torsten Ekedahl | timeline score: 4 | |
| Apr 24, 2010 at 9:03 | comment | added | Torsten Ekedahl | Not that this is an answer to your question (which is an interesting one) but you can hide the nasty details of the reduction to the Brouwer fixed point theorem by using the Michael selection theorem which gives a continuous map $f\colon S \to S$ with $f(x) \in \phi(x)$ for all $x$ to which you then can directly apply the Brouwer theorem. | |
| Apr 23, 2010 at 10:06 | comment | added | Tom Smith | Re. convexity: Economists tend to think of/be taught the Brouwer Theorem as being a statement about compact convex sets in $\mathbb{R}^n$ - then they don't need to be taught about homeomorphisms! | |
| Apr 23, 2010 at 3:00 | history | asked | Aaron Bergman | CC BY-SA 2.5 |