2016/10/11 by Miesch, Benjamin, Pavón, Maël
#FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG)
paper · doi:10.48550/arxiv.1610.03307
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.