International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 11, Pages 729-739
doi:10.1155/S0161171200003288
Quantifying completion
1Universiteit Antwerpen, Departement Wiskunde-informatica, Groenenborgerlaan 171, Antwerpen B-2020, Belgium
2Department of Mathematics and Computer Science, University of Antwerp, RUCA, Groenenborgerlaan 171, Antwerpen 2020, Belgium
Received 23 April 1999
Copyright © 2000 Robert Lowen and Bart Windels. 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
Approach uniformities were introduced in Lowen and Windels (1998)
as the canonical generalization of both metric spaces and uniform
spaces. This text presents in this new context of “quantitative” uniform spaces, a reflective completion theory which generalizes
the well-known completions of metric and uniform spaces. This
completion behaves nicely with respect to initial structures and
hyperspaces. Also, continuous extensions of pseudo-metrics on
uniform spaces and (real) compactification of approach spaces can
be interpreted in terms of this completion.