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

In this paper, we initiated new types of near open and closed sets called higher order sets. These sets generated by much iteration 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 of 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.