Boundaries of compact convex sets and fragmentability

If X is a compact convex set in a real locally convex space, B ⊂ X 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. © 2008 Elsevier Inc. All rights reserved.