Includes bibliographical references. / The relationship between transitive uniform spaces and zero-dimensional topological spaces was first established by Banaschewski [1957], and was later investigated by Levine [1969]. The theory of transitive quasi-uniform spaces is treated in [Fletcher and Lindgren 1972], [Brummer 1984] and [Kiinzi 1990, 1992a, 1992b,1993]; a convenient presentation for our purpose is to be found in [Fletcher and Lindgren 1982]. After Reilly [1972] introduced the notion of zero-dimensionality in bitopological spaces, Birsan [1974] and Halpin [1974] studied the relationship between transitive quasi-uniform spaces and zero-dimensional bitopological spaces. In this thesis we define a notion of zero-dimensionality in ordered topological spaces and examine the relationship between transitive quasi-uniform spaces and zero-dimensional ordered topological spaces. To a large extent, our presentation is influenced by the situation in bitopological spaces (cf. [Halpin 1974] and [Birsan 1974]), and uses the commutative diagrams which occur in [Schauerte 1988] and [Brummer 1977, 1982]. We also study strongly zero-dimensional ordered topological spaces and their relation with functorial quasi-uniformities. In this respect, our results are influenced by those of [Fora 1984], [Banaschewski and Brummer 1990] and [Kiinzi 1990] for strongly zero-dimensional bitopological spaces.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:uct/oai:localhost:11427/17403 |
| Date | January 1993 |
| Creators | Nailana, Kwena Rufus |
| Contributors | Brümmer, Guillaume C L |
| Publisher | University of Cape Town, Faculty of Science, Department of Mathematics and Applied Mathematics |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Master Thesis, Masters, MSc |
| Format | application/pdf |
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