International Journal of Mathematics and Mathematical Sciences
Volume 26 (2001), Issue 9, Pages 561-579

Quantification of topological concepts using ideals

Robert Lowen and Bart Windels

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

Received 19 February 2000

Copyright © 2001 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.


We introduce certain ideals of real-valued functions as a natural generalization of filters. We show that these ideals establish a canonical framework for the quantification of topological concepts, such as closedness, adherence, and compactness, in the setting of approach spaces.