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 the relationships among them as well as show that the full subcategories of the category of constant filter convergence spaces consisting of local T4 constant filter convergence spaces 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.