We investigate quotient-fine nearness frames, showing that they are reflective in the category
of strong nearness frames, and that, in those with spatial completion, any near subset
is contained in a near grill. We construct two categories, each of which is shown to be
equivalent to that of quotient-fine nearness frames. We also consider some subcategories of
the category of nearness frames, which are co-hereditary and closed under coproducts. We
give due attention to relations between these subcategories. We introduce totally strong
nearness frames, whose category we show to be closed under completions. We investigate
N-homomorphisms and remote points in the context of totally bounded uniform frames,
showing the role played by these uniform N-homomorphisms in the transfer of remote
points, and their relationship with C -quotient maps. A further study on grills enables
us to establish, among other things, that grills are precisely unions of prime filters. We
conclude the thesis by showing that the lattice of all nearnesses on a regular frame is a
pseudo-frame, by which we mean a poset pretty much like a frame except for the possible
absence of the bottom element. / Mathematical Sciences / Ph.D. (Mathematics)
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:unisa/oai:uir.unisa.ac.za:10500/2975 |
| Date | 09 1900 |
| Creators | Mugochi, Martin Mandirevesa |
| Contributors | Dube, T.A. (Prof.) |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | 1 online resource (vi, 113 p.) |
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