International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 1, Pages 1-18

A Unif: A common supercategory of pMET and Unif

R. Lowen and B. Windels

Department of Mathematics and Computer Science, University of Antwerp, RUCA Groenenborgerlaan 171, Antwerp 2020, Belgium

Received 17 July 1996; Revised 24 February 1997

Copyright © 1998 R. Lowen and B. 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.


In order to have a topological category that contains both pMET and Unif in a nice way (and therefore combines quantitative and uniform concepts), approach uniformities are introduced. Approach uniformities uniformize the so-called approach spaces, introduced in Lowen [8]. Different characterizations of approach uniformities are formulated. Some natural examples are presented, such as function spaces, hyperspaces, spaces of measures, and an example concerning theoretical computer science.