PS-regular sets in generalized topology

Abstract

In general topology, repeated applications of interior and closure operators give rise to several different new classes of sets. Someof them aregeneralized formof open setswhile few others are the so-called regular sets. These classes are foundto have applications not only inmathematics but even in diversefields outside the realm of mathematics [1–3]. Due to this, investigations of these sets have gainedmomentum in the recent days. Csaszar has already provided an umbrella study for generalized open sets in his latest papers [4–7]. In this paper, we introduce and study a new class of sets, called PS-regular sets, using semi-interior and semi-closure operators. Initially, we define them for a broader class, that is, for generalized topological spaces and discuss their various properties. Interrelationship of PS-regular setswith other existing classes such as semiopen sets, regular open sets, t-sets, α*-sets, B-sets, and C-sets has been studied. A characterization of semiconnectedness is also provided using PS-regular sets. Moreover, ξ-regular sets, where ξ∈ {α, β, π, σ}, of a generalized topological space are studied using PS-regular sets.