The Existence of Unbounded Closed Convex Sets with Trivial Recession Cone in Normed Spaces

被引：1

作者：

Huynh The Phung ^{[1
]}

机构：

[1] Hue Univ, Coll Sci, 77 Nguyen Hue St, Hue City, Vietnam

来源：

ACTA MATHEMATICA VIETNAMICA | 2016年 / 41卷 / 02期

关键词：

Recession cone; Bounded and linearly bounded; Convex set; Infinite-dimensional normed space;

D O I：

10.1007/s40306-015-0131-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It's well known that a closed convex set in a finite-dimensional normed space is unbounded if and only if it has a nonzero recession direction. In this work, we shall prove that in every infinite-dimensional normed space there exists an unbounded closed convex set whose recession cone consists of the zero vector alone.

引用

页码：277 / 282

页数：6

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