Boundaries of compact convex sets and fragmentability

Abstract: If X is a compact convex set in a real locally convex space, is said to be its boundary if every affine continuous function on X attains its maximum at some point of B. We study relations between fragmentability of B and the whole set X. As a byproduct we obtain a characterization of separable Asplund spaces. We also study the possibility of finding the Haar system in a boundary of a metrizable compact convex set. [Copyright &y& Elsevier]