Functorial quasi-uniformities over partially ordered spaces

• Main Author: Schauerte, Anneliese
• Other Authors: Brümmer, Guillaume C L
• Format: Dissertation
• Language: English
• Published: University of Cape Town 2016
• Subjects: Quasi-uniform spaces; Partially ordered spaces; Functor theory
• Online Access: http://hdl.handle.net/11427/22202

Bibliography: pages 90-94. === Ordered spaces were introduced by Leopoldo Nachbin [1948 a, b, c, 1950, 1965]. We will be primarily concerned with completely regular ordered spaces, because they are precisely those ordered spaces which admit quasi-uniform structures. A recent and convenient study of these spaces is in the book by P. Fletcher and W.F. Lindgren [1982]. In this thesis we consider functorial quasi-uniformities over (partially) ordered spaces. The functorial methods which we use were developed by Brummer [1971, 1977, 1979, 1982] and Brummer and Hager [1984, 1987] in the context of functorial uniformities over completely regular topological spaces, and of functorial quasi-uniformities over pairwise. completely regular bitopological spaces. We obtain results which are to a large extent analogous to results in those papers. We also introduce some functors which relate our functorial quasi-uniformities to the structures studied by Brummer and others (e.g. Salbany [1984]).