On the Krein-Milman theorem for convex compact metrizable sets
Résumé
The Krein-Milman theorem states that a convex compact subset of a Hausdorff locally convex topological space, is the closed convex hull of its extreme points. We prove that, in the metrizable case the situation is rather better. Indeed, 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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