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

by Craig, A.P.K.

Abstract (Summary)
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.
Bibliographical Information:

Advisor:

School:Rhodes University

School Location:South Africa

Source Type:Master's Thesis

Keywords:mathematics pure applied

ISBN:

Date of Publication:01/01/2008

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