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The horofunction boundary of finite-dimensional normed spaces

Published online by Cambridge University Press:  01 May 2007

CORMAC WALSH
CORMAC WALSH*
Affiliation:
INRIA, Domaine de Voluceau, 78153 Le Chesnay Cédex, France. e-mail: cormac.walsh@inria.fr
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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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 142 , Issue 3 , May 2007 , pp. 497 - 507
Copyright
Copyright © Cambridge Philosophical Society 2007

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