We show that the cardinality of a compact convex set W in a topological linear space X satisfies the condition that . We also establish some relations between the cardinality of W and that of extrW provided X is locally convex. Moreover, we deal with the cardinality of the convex set E(μ) of all quasi-measure extensions of a quasi-measure μ, defined on an algebra of sets, to a larger algebra of sets, and relate it to the cardinality of extrE(μ).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm123-1-10,
author = {Zbigniew Lipecki},
title = {Cardinality of some convex sets and of their sets of extreme points},
journal = {Colloquium Mathematicae},
volume = {122},
year = {2011},
pages = {133-147},
zbl = {1223.28002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm123-1-10}
}
Zbigniew Lipecki. Cardinality of some convex sets and of their sets of extreme points. Colloquium Mathematicae, Tome 122 (2011) pp. 133-147. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm123-1-10/