The horofunction boundary of finite-dimensional normed spaces

Cormac Walsh

doi:10.1017/s0305004107000096

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The horofunction boundary of finite-dimensional normed spaces

Cormac Walsh

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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 Painleve-Kuratowski topology.

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Cormac Walsh. 2006-06-29. The horofunction boundary of finite-dimensional normed spaces. https://doi.org/10.1017/s0305004107000096

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