Boundaries of compact convex sets and fragmentability |
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Authors: | Ond?ej FK Kalenda Ji?í Spurný |
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Institution: | Charles University, Faculty of Mathematics and Physics, Department of Mathematical Analysis, Sokolovská 83, 186 75 Praha 8, Czech Republic |
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Abstract: | 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. |
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Keywords: | Compact convex sets Boundary Extreme points Fragmentability Asplund spaces Haar system |
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