A converse to the Eidelheit theorem in real Hilbert spaces

被引：2
|
作者：
Ernst, E
Théra, M
机构：
[1] Fac Sci & Tech St Jerome, Lab Modelisat Mecan & Thermodynam, F-13397 Marseille, France
[2] Univ Limoges, LACO, F-87060 Limoges, France
来源：
BULLETIN DES SCIENCES MATHEMATIQUES | 2005年 / 129卷 / 05期
关键词：
convex separation; Hahn-Banach theorem; eidelheit theorem; compactly epi-lipschitzian sets;
D O I：
10.1016/j.bulsci.2004.11.002
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We establish the following converse to the Eidelheit theorem: an unbounded closed and convex set of a real Hilbert space may be separated by a closed hyperplane from every other disjoint closed and convex set, if and only if it has a finite codimension and a non-empty interior with respect to its affine hull. (c) 2004 Elsevier SAS. All rights reserved.
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页码：381 / 397
页数：17
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