Approach Merotopies and Associated Near Sets

This article introduces associated near sets of a collection of sets. The proposed approach introduces a means of defining as well as describing an ε-approach merotopy in terms of the members of associated sets of collections that are sufficiently near. A characterization for continuous functions is established using associated near sets. This article also introduces p-containment considered in the context of near sets. An application of the proposed approach is given in terms of digital image classification.