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International Journal of Mathematics and Mathematical Sciences
Volume 23, Issue 11, Pages 729-739
http://dx.doi.org/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 Hindawi Publishing Corporation. 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.