CARDINALITY OF SOME CONVEX SETS AND OF THEIR SETS OF EXTREME POINTS

被引:6
作者
Lipecki, Zbigniew [1 ]
机构
[1] Polish Acad Sci, Inst Math, Wroclaw Branch, PL-51617 Wroclaw, Poland
关键词
topological linear space; locally convex space; compact convex set; extreme point; cardinality; algebraic dimension; omega-power; Krein-Milman theorem; Choquet theory; algebra of sets; superatomic; quasi-measure; atomic; nonatomic; extension; scattered space; QUASI-MEASURES; EXTENSIONS; COMPACTNESS;
D O I
10.4064/cm123-1-10
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We show that the cardinality n of a compact convex set W in a topological linear space X satisfies the condition that n(aleph 0) = n. We also establish some relations between the cardinality of W and that of extr W provided X is locally convex. Moreover, we deal with the cardinality of the convex set E(mu) of all quasi-measure extensions of a quasi-measure mu, defined on an algebra of sets, to a larger algebra of sets, and relate it to the cardinality of extr E(mu).
引用
收藏
页码:133 / 147
页数:15
相关论文
共 25 条
  • [1] [Anonymous], MATH Z
  • [2] [Anonymous], 1966, Lectures on Choquet's theorem
  • [3] [Anonymous], COLLECT MATH
  • [4] Carreras P. Perez, 1987, BARRELLED LOCALLY CO
  • [5] Comport W.W., 1971, GEN TOPOL APPL, V1, P163
  • [6] Dunford N, 1958, Linear operators, part I: general theory
  • [7] Engelking R., 1977, GEN TOPOLOGY
  • [8] Fremlin D. H., 2003, Bulletin of the Polish Academy of Sciences, Technical Sciences, V51, P169
  • [9] FUCHSSTEINER B, 1974, J FUNCT ANAL, V17, P377
  • [10] EXTREME POINT CRITERION FOR SEPARABILITY OF A DUAL BANACH-SPACE, AND A NEW PROOF OF A THEOREM OF CORSON
    HAYDON, R
    [J]. QUARTERLY JOURNAL OF MATHEMATICS, 1976, 27 (107) : 379 - 385