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 T ¯ 0 , local T 0 ′ , 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.
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