theta_sw-continuity of maps in the product space and some versions of separation axioms

Abstract

In this study, the concept of theta_sw-open set is introduced and its relationship to the other well-known concepts such as the classical open, theta-open, and omega_theta-open sets is described. The concepts of theta_sw-interior and theta_sw-closure of a set is also defined and investigated. Related concepts such as theta_sw-open and theta_sw-closed functions, theta_sw-continuous function, theta_sw-connected, and some versions of separation axioms are defined and characterized. Finally, the concept of theta_sw-continuous function from an arbitrary topological space into the product space is investigated further.