Quasi-metric tree in T0-quasi-metric spaces

In his well-known paper dealing with metric trees and tight extension of metric spaces, Dress studied the relationship between metric trees and hyperconvex metric spaces. In the present work, we introduce similarly the notion of quasi-metric tree of a T0-quasi-metric space. In particular, we show that large parts of the theory of metric trees do not use the symmetry of the metric and, under appropriate modifications, it still holds essentially unchanged for T0-quasi-metrics.