Measure of Compactness for Filters in the Approach Setting
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.
Mynard, Frédéric D..
"Measure of Compactness for Filters in the Approach Setting."
Quaestiones Mathematicae, 31 (3): 189-201.
doi: 10.2989/QM.2008.31.3.1.543 source: http://www.tandfonline.com/doi/abs/10.2989/QM.2008.31.3.1.543?journalCode=tqma20#.VBrmLpRdWuI