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.

Keywords: measure of compactness; compactness for filters; approach spaces; convergence
approach spaces; reflections in convergence-approach spaces

Quaestiones Mathematicae 31(2008), 189–201