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

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