Construction of quasi-metrics determined by orders
Doctoral Thesis
2016
Permanent link to this Item
Authors
Supervisors
Journal Title
Link to Journal
Journal ISSN
Volume Title
Publisher
Publisher
University of Cape Town
Faculty
License
Series
Abstract
The second half of the last century has seen a growing interest in the area of quasi-pseudometricspaces and related asymmetric structures. Problems arising from theoretical computer science, applied physics and many more areas can easily be expressed in that setting. In the asymmetric framework, many investigations on general topology have been done in order to extend known results of the classical theory. It is the aim of this thesis to dig more into this theory by investigating the existence of quasi-pseudometrics that produce a given partially ordered metric space. We show that whenever one has an ordered metric space, it is often possible to describe both the metric and the order using quasi-pseudometrics. We establish respectively topological and algebraic conditions for the existence of such quasi-pseudometrics.We deduct some specific conditions when the ordered metric space(X; m,≤) is assumed to have some topological properties such as compactness. When a producing quasi-pseudo metric exists, the question of uniqueness is also studied. A characterization of produced spaces is given.
Description
Reference:
Gaba, Y. 2016. Construction of quasi-metrics determined by orders. University of Cape Town.