Endpoints in T 0 -Quasimetric Spaces: Part II

Abstract

We continue our work on endpoints and startpoints in $T_0$-quasimetric spaces. In particular we specialize some of our earlier results to the case of two-valued $T_0$-quasimetrics, that is, essentially, to partial orders. For instance, we observe that in a complete lattice the startpoints (resp., endpoints) in our sense are exactly the completely join-irreducible (resp., completely meet-irreducible) elements. We also discuss for a partially ordered set the connection between its Dedekind-MacNeille completion and the $q$-hyperconvex hull of its natural $T_0$-quasimetric space.