Open Collections

Abstract

The Krein-Milman Theorem says that each compact, convex subset of a locally convex space is the closed convex hull of its extreme points. In the case of a separable Banach Space several collections of extreme points are known to be dense in the whole set of extreme points (e.g. the set of exposed points [5; theorem 4]; the set of denting points [8; remarks following definition 44]). Consequently these sets can be used instead of the whole set of extreme points to generate compact convex sets. In this thesis we examine such a dense subset of extreme points in the context of less structured separable locally convex spaces. We also examine some applications of the resulting extended Krein-Milman Theorem.