T4 , Urysohn’s lemma, and Tietze extension theorem for constant filter convergence spaces

Abstract

In this paper, we characterize various local forms of T4 constant filter convergence spaces and investigate therelationships among them as well as showing that the full subcategories of the category of constant filter convergencespaces consisting of local T4 constant filter convergence spaces that are hereditary. Furthermore, we examine therelationship between local T4 and general T4 constant filter convergence spaces. Finally, we present Urysohn’s lemmaand Tietze extension theorem for constant filter convergence spaces.