The horofunction boundary of finite-dimensional normed spaces
The horofunction boundary of finite-dimensional normed spaces
复制标题
有限维赋范空间的星函数边界
DOI：
10.1017/s0305004107000096
复制
发表时间：
2005
影响因子：
0.8
通讯作者：
C. Walsh
中科院分区：
文献类型：
--
作者：
C. Walsh
摘要我们确定了任意有限维赋范空间的Busemann点集。这些是函数边界上的点，它们是“近测地线”的极限。当且仅当对偶单位球的极值集在painlev<s:1> - kuratowski拓扑中闭合时，证明函数边界上的所有点都是Busemann点。
Abstract 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 Painlevé–Kuratowski topology.