Endpoints in \(T_0\)-quasimetric spaces. II.
The authors continue their study of endpoints and the q-hyperconvex hull of a \(T_0\)-quasimetric space, initiated in [\textit{C. A. Agyingi} et al., Topology Appl. 168, 82--93 (2014; Zbl 1292.54016)]. In this paper, they study the concept of collinearity in quasi-pseudometric spaces and show that for a join compact \(T_0\)-quasimetric space, the points in the remainder of its q-hyperconvex hull lie between a startpoint and an endpoint of the space. They also prove that the q-hyperconvex hull of a join compact \(T_0\)-quasi-metric space has the same endpoints and startpoints as the space. Then they study startpoints and endpoints in the natural \(T_0\)-quasimetric of a partially ordered set, giving a characterization in terms of the partial order and providing various examples for different partially ordered sets. Finally, the authors study the relation between the MacNeille completion of a partially ordered set and the q-hyperconvex hull of its natural \(T_0\)-quasimetric.
scientific article; zbMATH DE number 6306986
scientific article