Hyperconvexity and Metric Trees

2007/02/05 by Asuman Güven Aksoy, A. G. Aksoy, Aksoy, A. G. +3
Computer Science · Mathematics · #Advanced Graph Theory Research #Advanced Optimization Algorithms Research #Complexity and Algorithms in Graphs #math.FA #math.MG #msc:46M10 #msc:54H12

paper · pdf · doi:10.48550/arxiv.math/0702125

11 pages

arxiv created 2007/02/05 · arxiv updated 2009/12/01

Abstract

In this paper we examine the relationship between hyperconvex hulls and metric trees. After providing a linking construction for hyperconvex spaces, we show that the four-point property is inherited by the hyperconvex hull, which leads to the theorem that every complete metric tree is hyperconvex. We also consider some extension theorems for these spaces.

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