Sequences of topological near open and near closed sets with rough applications

Abstract

In this paper, we initiated new types of near open and closed sets called high order sets. These sets generated by many iterations of topological interior and closure operations for a given set.  These new sets are the terms of many sequences of topological near open and near closed sets. We studied many generalizations to the classical near open sets to these sequences.  This paper is the starting point of a new way for researchers to study the high order topology.