Higher Connectedness Properties of Support Points and Functionals of Convex Sets

被引：0
|
作者：
De Bernardi, Carlo Alberto [1 ]
机构：
[1] Univ Milan, Dipartimento Matemat, I-20133 Milan, Italy
来源：
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES | 2013年 / 65卷 / 06期
关键词：
Absolute retract; Convex set; Leray-Schauder continuation principle; Support functional; Support point;
D O I：
10.4153/CJM-2012-048-8
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove that the set of all support points of a nonempty closed convex bounded set C in a real infinite-dimensional Banach space X is AR(sigma-compact) and contractible. Under suitable conditions, similar results are proved also for the set of all support fiinctionals of C and for the domain, the graph, and the range of the subdifferential map of a proper convex lower semicontinuous function on X.
引用
收藏
页码：1236 / 1254
页数：19
相关论文
共 50 条
12345