Endpoints in T0T0-quasi-metric spaces

In his well-known paper dealing with the construction of the injective hull of a metric space Isbell introduced the concept of an endpoint of a (compact) metric space.In the present article we introduce similarly the notion of an endpoint in a (joincompact) T0T0-quasi-metric space. It turns out that in a (joincompact) T0T0-quasi-metric space there is a dual concept which we shall call a startpoint. With the help of these concepts we are able to generalize some of the classical results on endpoints in metric spaces to the quasi-metric setting.