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## Complete regularity and related concepts in L-uniform spaces

L will denote a completely distributive lattice with an order reversing involution. The concept of an L-uniform space is introduced. An extension theorem concerning L-uniformly continuous functions is proved. A characterisation of L-uniformizability, involving L-complete regularity is given. With respect to L--completely regular spaces it is shown that the topological modification of an L-completely regular space is completely regular. Furthermore it is shown that the topologically generated L-topology of a completely regular space is L-completely regular.

Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:rhodes/vital:5403 |

Date | January 1992 |

Creators | Harnett, Rait Sicklen |

Publisher | Rhodes University, Faculty of Science, Mathematics |

Source Sets | South African National ETD Portal |

Language | English |

Detected Language | English |

Type | Thesis, Masters, MSc |

Format | 151 p., pdf |

Rights | Harnett, Rait Sicklen |

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