The horofunction boundary of finite-dimensional normed spaces

被引：27

作者：

Walsh, Cormac ^{[1
]}

机构：

[1] Inst Natl Rech Informat & Automat, F-78153 Le Chesnay, France

来源：

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY | 2007年 / 142卷

关键词：

D O I：

10.1017/S0305004107000096

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We determine the set of Busemann points of an arbitrary finite-dimensional normed space. These are the points of the horofunction boundary that are the limits of "almost-geodesics". We prove that all points in the horofunction boundary are Busemann points if and only if the set of extreme sets of the dual unit ball is closed in the Painleve-Kuratowski topology.

引用

页码：497 / 507

页数：11

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