Metric Trees , Hyperconvex Hulls and Extensions

  title={Metric Trees , Hyperconvex Hulls and Extensions},
  author={Asuman G{\"u}ven Aksoy and Brian Maurizi},
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.