The horofunction boundary of finite-dimensional normed spaces
Geometric Topology
2009-04-23 v3 Metric Geometry
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 Painleve-Kuratowski topology.
Keywords
Cite
@article{arxiv.math/0510105,
title = {The horofunction boundary of finite-dimensional normed spaces},
author = {Cormac Walsh},
journal= {arXiv preprint arXiv:math/0510105},
year = {2009}
}
Comments
11 pages v2. Some proofs streamlined and another example added