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## Functorial quasi-uniformities over partially ordered spaces

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]).

Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:uct/oai:localhost:11427/22202 |

Date | January 1988 |

Creators | Schauerte, Anneliese |

Contributors | BrÃ¼mmer, 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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