Cardinality of some convex sets and of their sets of extreme points

Zbigniew Lipecki. "Cardinality of some convex sets and of their sets of extreme points." Colloquium Mathematicae 123.1 (2011): 133-147. <http://eudml.org/doc/283589>.

@article{ZbigniewLipecki2011,
abstract = {We show that the cardinality of a compact convex set W in a topological linear space X satisfies the condition that $^\{ℵ₀\} = $. 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).},
author = {Zbigniew Lipecki},
journal = {Colloquium Mathematicae},
keywords = {topological linear space; locally convex space; compact convex set; extreme point; algebraic dimension; -power; Kreĭn-Milman theorem; Choquet theory; superatomic; quasi-measure; atomic; nonatomic; scattered space},
language = {eng},
number = {1},
pages = {133-147},
title = {Cardinality of some convex sets and of their sets of extreme points},
url = {http://eudml.org/doc/283589},
volume = {123},
year = {2011},
}

TY - JOUR
AU - Zbigniew Lipecki
TI - Cardinality of some convex sets and of their sets of extreme points
JO - Colloquium Mathematicae
PY - 2011
VL - 123
IS - 1
SP - 133
EP - 147
AB - We show that the cardinality of a compact convex set W in a topological linear space X satisfies the condition that $^{ℵ₀} = $. 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).
LA - eng
KW - topological linear space; locally convex space; compact convex set; extreme point; algebraic dimension; -power; Kreĭn-Milman theorem; Choquet theory; superatomic; quasi-measure; atomic; nonatomic; scattered space
UR - http://eudml.org/doc/283589
ER -