T$_{4}$, Urysohn's lemma, and Tietze extension theorem for constant filter convergence spaces

Authors: TESNİM MERYEM BARAN, AYHAN ERCİYES

Abstract: In this paper, we characterize various local forms of T$_{4}$ 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 T$_{4}$ constant filter convergence spaces that are hereditary. Furthermore, we examine the relationship between local T$_{4}$ and general T$_{4}$ constant filter convergence spaces. Finally, we present Urysohn's lemma and Tietze extension theorem for constant filter convergence spaces.

Keywords: Topological category, T$_{4}$ objects, T$_{4}$ objects, constant filter convergence spaces

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