Quasi-metric trees and q-hyperconvex hulls

Abstract

The investigation of metric trees began with J. Tits in 1977. Recently we studied a more general notion of quasi-metric tree. In the current article we prove, among other facts, that the q-hyperconvex hull of a q-hyperconvex T0-quasi-metric tree is itself a T0-quasi-metric tree. This is achieved without using the four-point property, a geometric concept used by Aksoy and Maurizi to show that every complete metric tree is hyperconvex.