Separation and connectedness in the category of constant filter convergence spaces

Abstract

The purpose of this work is to introduce two notions of closure in the category ConFCO of constant filter convergence spaces with continuous maps and investigate whether they satisfy the idempotency, productivity, (weak) hereditariness, and (full) additiveness as well as examine how they are related to each other. Moreover, we characterize each of T_i, i = 1, 2 spaces with respect to these closures and examine
epimorphisms in the subcategories of ConFCO. Furthermore, we give the characterization of connected constant filter convergence spaces and investigate some invariance properties of them. Finally, we compare our results with results in some other topological categories.