Research Article

Approximation and Compactness

Published in: Quaestiones Mathematicae
Volume 49 , issue 1 , 2026 , pages: 79–118

DOI: 10.2989/16073606.2025.2557863

Author(s): E. Colebunders Vrije Universiteit Brussel, België , R. Lowen Universiteit Antwerpen, België

Keywords: 54A05 , 54D30 , 54E35 , 54E40 , 54E45 , 54E99 , Metric space , non-expansive map , asymptotic center , Opial’s condition , approach space , contraction , limit operator , adherence operator , compactness , ultrafilter-compactness , filter-compactness , ultrafilter-closure , filter-closure , ultrafilter-separated , preservation under subspace , product and coproduct , preservation by maps , one point ultrafilter-compactification

Download full text Get new issue alerts

Abstract

In approach theory convergence is described by means of limit and adherence operators acting on filters or ultrafilters. The value of the limit resp. adherence operator on an (ultra)filter in a point x is interpreted as the distance that the point x is away from being a limit resp. an adherence point of the (ultra)filter. A point were a limit resp. adherence operator attains its minimal value, if it exists, hence is a point which comes closest to being a limit or adherence point of the given filter.

« Corrigendum to “Asymptotical convergence of solutions of boundary value problems for singularly perturbed higher-order integro-differential equations” Quaestiones Mathematicae, 47(11) (2024), 2231–2246.

The role of concave functions in the study of interpolative contractions »