On the Krein-Milman theorem for convex compact metrizable sets
Résumé
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.
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