[Banach] Abstract of a paper by Mohammed Bachir

This is an announcement for the paper “On the Krein-Milman theorem for convex compact metrizable sets” by Mohammed Bachir.

Abstract: The Krein-Milman theorem (1940) states that a convex compact subset of a Hausdorff locally convex topological space, is the closed convex hull of its extreme points. We prove in this paper that in the metrizable case, the situation is better: every convex compact metrizable subset of a Hausdorff locally convex topological space, is the closed convex hull of its exposed points. This fails in general for not metrizable compact convex subsets.

The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1604.08473