About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 539573, 10 pages
http://dx.doi.org/10.1155/2013/539573
Research Article

Endpoints in -Quasimetric Spaces: Part II

Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701, South Africa

Received 26 May 2013; Accepted 15 July 2013

Academic Editor: Salvador Hernandez

Copyright © 2013 Collins Amburo Agyingi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.