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arXiv · 1610.03307

Ball Intersection Properties in Metric Spaces

Benjamin Miesch·Maël Pavón
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Abstract

We show that in complete metric spaces, $4$-hyperconvexity is equivalent to finite hyperconvexity. Moreover, every complete, almost $n$-hyperconvex metric space is $n$-hyperconvex. This generalizes among others results of Lindenstrauss and answers questions of Aronszajn-Panitchpakdi. Furthermore, we prove local-to-global results for externally and weakly externally hyperconvex subsets of hyperconvex metric spaces and find sufficient conditions in order for those classes of subsets to be convex with respect to a geodesic bicombing.

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Benjamin Miesch, Maël Pavón. 2016-10-11. Ball Intersection Properties in Metric Spaces. https://arxiv.org/abs/1610.03307

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