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

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