The horofunction boundary of finite-dimensional normed spaces

Details The horofunction boundary of finite-dimensional normed spaces The horofunction boundary of finite-dimensional normed spaces

2005-10-05

arxiv.org/abs/math/0510105v3

Math. Proc. Camb. Phil. Soc, 142 (3) 497-507, 2007

Mathematics

Geometric Topology

11 pages v2. Some proofs streamlined and another example added

Scientific paper

10.1017/S0305004107000096

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.

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