Approach Merotopies and Near Filters Theory and Application

This article considers the problem of how approach spaces can be used in the study of near lters, in general, and descriptively near lters, in particular. The solution to the problem stems from recent work on approach spaces, approach merotopies, near lters, descriptively near sets, and a specialised form of merotopy de ned in terms of a variation of the  Cech gap functional in measuring the distance between nonempty sets. A nonempty set equipped with a distance function satisfying certain properties is an approach space. This article investigates the theory and application of merotopies and near lters in terms of the nearness of digital images