Extreme points and geometric aspects of compact convex sets in asymmetric normed spaces

Abstract

The Krein–Milman theorem states that every compact convex subset in a locally compact convex space is the closure of the convex hull of its extreme points. Inspired by this result, we investigate the existence of extreme points in compact convex subsets of asymmetric normed spaces. We focus our attention in the finite dimensional case, giving a geometric description of all compact convex subsets of a finite dimensional asymmetric normed space.