On the MacNeille Completion of the Category of Partially Ordered Topological Spaces

Preordered topological spaces for which the order has a closed graph form a topological category. Within this category we identify the MacNeille completions (coinciding with the universal initial completions) of five monotopological subcategories, namely those of the T₀(T₁, T₂) preordered spaces and the (completely regular) partially ordered spaces. We also show that a functor due to L. NACHBIN from the quasi-uniform spaces to the preordered spaces preserves initial sources.