Modifications to Mixed θ(ν1, ν2)-open Sets inGeneralized Topological Spaces

A. Cs´asz´ar and Makai Jr. [5] introduced the concepts of the mixed operation γθ(ν1,ν2) and mixed θ(ν1, ν2)-open sets in generalized topological spaces. In this paper, we extend this framework by introducing the concepts of mixed operation γ˜θ(ν1,ν2) and mixed ˜θ(ν1, ν2)-open sets (briefly, ˜θ(ν1, ν2)- open sets) and investigate their fundamental properties in generalized topological spaces. We explore the relationships among γ˜θ(ν1,ν2), γθ(ν1,ν2), and γθ(ν), as well as the relationships among ˜θ(ν1, ν2)-open sets, θ(ν1, ν2)-open sets, and μ-open sets. Additionally, we introduce the notion of G(ν1, ν2)-regularity in generalized topological spaces. Finally, we provide characterizations of ˜θ(ν1, ν2)-open sets using mixed G(ν1, ν)-regular concept