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 filters, in general, and descriptively near filters, in particular. The solution to the problem stems from recent work on approach spaces, approach merotopies, near filters, descriptively near sets, and a specialised form of merotopy defined in terms of a variation of the C̆ech 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 filters in terms of the nearness of digital images.