Mathematical Sciences: Faculty Publications

Measure of Compactness for Filters in the Approach Setting

Document Type

Article

Publication Date

2008

Publication Title

Quaestiones Mathematicae

DOI

10.2989/QM.2008.31.3.1.543

Abstract

New explicit descriptions of the reflections of a convergence-approach space on pseudo-approach, pre-approach and approach spaces are given. A measure of compactness for filters is introduced in the context of convergence-approach spaces. It is shown that this measure generalizes all the known measures of variants of compactness and can also be used to describe the reflections mentioned above.

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