On support points and support functionals of convex sets

被引：0
|
作者：
C. De Bernardi
L. Veselý
机构：
[1] Università degli Studi,Dipartimento di Matematica
来源：
Israel Journal of Mathematics | 2009年 / 171卷
关键词：
Convex Cone; Continuous Curve; Support Point; Nonempty Interior; Continuous Selection;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Let K be a bounded closed convex subset of a real Banach space of dimension at least two. Then the set of the support points of K is pathwise connected and the set Σ1(K) of the norm-one support functionals of K is uncountable in each nonempty open set that intersects the dual unit sphere. In particular, the set Σ 1(K) is always uncountable, which answers a question posed by L. Zajíček.
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