The horofunction boundary of finite-dimensional normed spaces

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.

11 pages v2. Some proofs streamlined and another example added

References in corpus (3)

• The max-plus Martin boundary
• Group C*-algebras as compact quantum metric spaces
• Ideal closures of Busemann space and singular Minkowski space

Cited by in corpus (14)

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• The horofunction boundary of finite-dimensional ${\ell }_p$ spaces
• Idempotent and tropical mathematics and problems of mathematical physics (Volume II)
• Characterizing the metric compactification of $L_p$ spaces by random measures
• Horofunction compactifications and duality
• A metric version of Poincaré's theorem concerning biholomorphic inequivalence of domains
• Horofunction compactifications of symmetric cones under Finsler distances
• Firm non-expansive mappings in weak metric spaces
• Nonexpansive maps with surjective displacement
• Horofunctions and metric compactification of noncompact Hermitian symmetric spaces
• Subinvariant metric functionals for nonexpansive mappings