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## Lattice-valued uniform convergence spaces the case of enriched lattices

Using a pseudo-bisymmetric enriched cl-premonoid as the underlying lattice, we examine different categories of lattice-valued spaces. Lattice-valued topological spaces, uniform spaces and limit spaces are described, and we produce a new definition of stratified lattice-valued uniform convergence spaces in this generalised lattice context. We show that the category of stratified L-uniform convergence spaces is topological, and that the forgetful functor preserves initial constructions for the underlying stratified L-limit space. For the case of L a complete Heyting algebra, it is shown that the category of stratified L-uniform convergence spaces is cartesian closed.

Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:rhodes/vital:5411 |

Date | January 2008 |

Creators | Craig, Andrew Philip Knott |

Publisher | Rhodes University, Faculty of Science, Mathematics |

Source Sets | South African National ETD Portal |

Language | English |

Detected Language | English |

Type | Thesis, Masters, MSc |

Format | 122 p,, pdf |

Rights | Craig, Andrew Philip Knott |

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