标题： 度量空间中的球体交集性质 显示英文标题

标题： Ball Intersection Properties in Metric Spaces

摘要： 我们证明在完备度量空间中，$4$-超凸性等价于有限超凸性。 此外，每个完备的几乎$n$-超凸度量空间都是$n$-超凸的。 这推广了Lindenstrauss的结果，并回答了Aronszajn-Panitchpakdi的问题。 此外，我们证明了超凸度量空间中外部和弱外部超凸子集的局部到整体结果，并找到了这些子集相对于测地双组合为凸的充分条件。 显示英文摘要

摘要： 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.