Timeline for Compact Convex sets and Extreme Points
Current License: CC BY-SA 2.5
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 3, 2014 at 19:02 | comment | added | petrbel | There are examples that show the set of extreme points of a compact convex subset of a locally convex topological vector space need not be closed when the real dimension of the space is at least 3 - is that so? Where can one find some example of that set? For me it seems impossible to exists. | |
| Apr 3, 2011 at 20:43 | comment | added | Greg Kuperberg | @Pete For instance, the convex hull of the four points $(\pm 1, \pm 1, 0)$ and the unit circle in the $x$-$z$ plane. | |
| Jan 25, 2010 at 14:45 | answer | added | Ady | timeline score: 1 | |
| Jan 5, 2010 at 16:55 | comment | added | Pete L. Clark | Thanks for your responses. I deleted my original question, which was rather silly: somehow, in your perfectly clear 2.5 line answer, I missed the part where you used the 2-dimensionality. But I think it's good to have an example of the failure of closedness in higher dimensions. | |
| Jan 5, 2010 at 14:11 | comment | added | Harald Hanche-Olsen | Retagged the question – banach-spaces out, convexity in. | |
| Jan 5, 2010 at 14:10 | history | edited | Harald Hanche-Olsen |
edited tags
|
|
| Jan 5, 2010 at 8:01 | vote | accept | Mike Hartglass | ||
| Jan 5, 2010 at 8:01 | vote | accept | Mike Hartglass | ||
| Jan 5, 2010 at 8:01 | |||||
| Jan 5, 2010 at 7:38 | answer | added | 002 | timeline score: 9 | |
| Jan 5, 2010 at 7:14 | history | asked | Mike Hartglass | CC BY-SA 2.5 |