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 live 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.