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

• Autorzy: Zbigniew Lipecki
• Języki publikacji: EN

Abstrakty

EN

We show that the cardinality 𝔫 of a compact convex set W in a topological linear space X satisfies the condition that $𝔫^{ℵ₀} = 𝔫$. 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).

Kategorie tematyczne

• 46A55: Convex sets in topological linear spaces; Choquet theory
• 28A12: Contents, measures, outer measures, capacities
• 52A07: Convex sets in topological vector spaces
• 28A33: Spaces of measures, convergence of measures

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2011
• Tom: 123
• Numer: 1
• Strony: 133-147

Daty

wydano

2011

Twórcy

autor

Zbigniew Lipecki

• Institute of Mathematics, Polish Academy of Sciences, Wrocław Branch, Kopernika 18, 51-617 Wrocław, Poland

Identyfikatory

DOI

10.4064/cm123-1-10