We continue our work on endpoints and startpoints in -quasimetric spaces. In particular we specialize some of our earlier results to the case of two-valued -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 -hyperconvex hull of its natural -quasimetric space.
"Endpoints in -Quasimetric Spaces: Part II." Abstr. Appl. Anal. 2013 (SI57) 1 - 10, 2013. https://doi.org/10.1155/2013/539573