The horofunction boundary of finite-dimensional normed spaces

Cormac Walsh

doi:10.1017/S0305004107000096

The horofunction boundary of finite-dimensional normed spaces

Cormac Walsh

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	497-507
Number of pages	11
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
Volume	142
Issue number	3
DOIs	https://doi.org/10.1017/S0305004107000096
Publication status	Published - 1 May 2007

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AB - 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.

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JO - Mathematical Proceedings of the Cambridge Philosophical Society

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The horofunction boundary of finite-dimensional normed spaces

Abstract

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