Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4658059 | Topology and its Applications | 2016 | 18 Pages |
Abstract
We continue our investigation on those (partially) ordered metric spaces (X,m,≤)(X,m,≤) for which there exists a T0T0-quasi-metric d on X such that sup{d,d−1}=msup{d,d−1}=m and for any x,y∈Xx,y∈X we have that x≤yx≤y if and only if d(x,y)=0d(x,y)=0. In particular such partially ordered metric spaces are determined (in the sense of Nachbin) by a T0T0-quasi-uniformity with a countable base.We show that the compatibility conditions obtained in an earlier study between partial order and metric on the investigated spaces X become more transparent when additional compatibility conditions between metric and partial order with appropriate algebraic operations on X are assumed to hold.
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
Yaé Ulrich Gaba, Hans-Peter A. Künzi,