A note on quotient reflective subcategories of O-REL (Q2158399)

Summary: 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 \textbf{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 \textbf{O-REL}.