A new Class Between _-open Sets and -open sets in Generalized Topological Spaces

The concepts of an operation _ and _-open (_-closed) set on generalized topological space (GTS) were introduced by Won Keun Min a13. In this paper, we introduce and study an operation _ as a new operation in GTS. Some relationships between this new operation and each of _ operation and -closure operator are obtained. Moreover, we give some sufficient conditions for the equivalence between _ operation and _ operations, and between _ and -closure operator. We use the _-closure operator to introduce _-open sets as a new class of sets and we prove that this class of sets lies strictly between the class of -open sets and the class of _-open sets. Several properties of _-open sets and connections to other well-known generalized open sets are discussed.