A Note on Quotient Reflective Subcategories of O-REL

Abstract

In this paper, we examine the category of ordered-RELspaces. We show that it is a normalized and geometric topological category and give the characterization of local ${\overline{T}}_0$ , local $T_0^{\prime }$ , and local $T_1$ ordered-RELspaces. Furthermore, we characterize explicitly several notions of $T_0$ ’s and $T_1$ objects in O-REL and study their mutual relationship. Finally, it is shown that the category of $T_0$ ’s (resp. $T_1$ ) ordered-RELspaces are quotient reflective subcategories of O-REL.