|
|
|
|
exposed points are dense in the extreme points
|
(Theorem)
|
|
Theorem 1 (Strasziewicz) Let $K \subset {\mathbb{R}}^n$ be a closed convex set. Then the set of exposed points is dense in the set of extreme points.
For example, let $C(p)$ denote the closed ball in ${\mathbb{R}}^2$ of radius 1 and centered at $p.$ Then take $K$ to be the convex hull of $C(-1,0)$ and $C(1,0)$ The points $(-1,1),$ $(-1,-1),$ $(1,1),$ and $(1,-1)$ are extreme points, but they are not exposed points.
|
"exposed points are dense in the extreme points" is owned by jirka.
|
|
(view preamble | get metadata)
See Also: extreme point
| Other names: |
Strasziewicz theorem |
| Also defines: |
exposed point |
|
|
Cross-references: convex hull, radius, closed ball, extreme points, dense in, intersection, hyperplane, point, convex set, closed
This is version 1 of exposed points are dense in the extreme points, born on 2007-12-12.
Object id is 10124, canonical name is ExposedPointsAreDenseInTheExtremePoints.
Accessed 1294 times total.
Classification:
| AMS MSC: | 52A99 (Convex and discrete geometry :: General convexity :: Miscellaneous) |
|
|
|
|
|
|
Pending Errata and Addenda
|
|
|
|
|
|
|
|
|
|
|
