θβ-Open Sets and θβ-Continuous Functions in the Product Space

Abstract

In this paper, we introduced and characterized a new class of open set called θ_β-open set. Notably, the collection of all θ_β-open sets forms a topology. We then examined the relationship between θ_β-open sets and other well-known concepts, such as classical open sets, θ-open sets, and β-open sets. Additionally, we defined and investigated the concepts of θ_β-interior and θ_β-closure of a set, as well as θ_β-open functions, θ_β-closed functions, θ_β-continuous functions, and θ_β-connectedness. Finally, we present characterizations of θ_β-continuous functions from an arbitrary topological space into the product space, along with some versions of separation axioms.