Timeline for Is every compact convex set covered by a Choquet simplex?
Current License: CC BY-SA 4.0
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| May 28, 2023 at 21:16 | comment | added | Bruce Blackadar | I have found a counterexample to the uniqueness statement in the case where $\partial_e(K)$ is not closed. Roughly speaking, let $K$ be a compact convex set with a sequence of extreme points, such that the convex hull of the first four is a square and the sequence of extreme points converges to the center of the square. There are many nonisomorphic Choquet simplexes which cover $K$. | |
| May 28, 2023 at 18:29 | comment | added | Bruce Blackadar | It is not hard to show the answer is yes if $\partial_e(K)$ is closed. The tricky case is when the set of extreme points of $K$ is not closed. | |
| May 27, 2023 at 21:30 | history | asked | Bruce Blackadar | CC BY-SA 4.0 |