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.
Hyperconvex spaces, metric trees, extensions
AKSOY, ASUMAN G. and MAURIZI, B. (2008) "Metric Trees, Hyperconvex Hulls and Extensions," Turkish Journal of Mathematics: Vol. 32: No. 2, Article 8. Available at: https://journals.tubitak.gov.tr/math/vol32/iss2/8