Theta_beta-Open Sets and theta_beta-Continuous Functions in the Product Space

Abstract

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