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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.

Identiferoai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:rhodes/vital:5411
Date January 2008
CreatorsCraig, Andrew Philip Knott
PublisherRhodes University, Faculty of Science, Mathematics
Source SetsSouth African National ETD Portal
LanguageEnglish
Detected LanguageEnglish
TypeThesis, Masters, MSc
Format122 p,, pdf
RightsCraig, Andrew Philip Knott

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