(untitled) (European Journal of Pure and Applied Mathematics, 2025)
In [1], Kim and Min introduced the operation γ_* and H(θ)-open sets within the context of generalized topological spaces, utilizing a hereditary class H. In this study, we extend these concepts by employing two generalized topologies, μ and u, along with a hereditary class H. Specifically, we introduce and investigate the mixed operation γ_*(μ, u) (denoted briefly as γ_*(μ, u)) and the mixed H(θ(μ, u))-open sets (denoted as H(θ(μ, u))-open sets). We explore the interrelationships between γ_*(μ, u), γ_*, and the μ-closure, as well as the connections between H(θ(μ, u))-open sets, θ(μ, u)-open sets, and μ-open sets. Additionally, we define the concepts of Hr(μ, u)-regular open sets and H(μ, u)-regular open sets. Finally, we examine properties and characterizations of H(θ(μ, u))-open sets in terms of Hr(μ, u)-regular open sets and H(μ, u)-regular open sets.