The horofunction boundary of finite-dimensional normed spaces

• Autores: Cormac Walsh
• Localización: Mathematical proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, Vol. 142, Nº 3, 2007, págs. 497-507
• Idioma: inglés
• DOI: 10.1017/s0305004107000096
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• Resumen

  • 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.