International Journal of Mathematics and Mathematical Sciences
Volume 26 (2001), Issue 9, Pages 561-579
doi:10.1155/S0161171201005439

Quantification of topological concepts using ideals

Abstract

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.