Lattice-valued uniform convergence spaces the case of enriched lattices

Title: Lattice-valued uniform convergence spaces the case of enriched lattices
Creator: Craig, Andrew Philip Knott
ThesisAdvisor: Jäger, G.
Subject: Lattice theory
Subject: Uniform spaces
Subject: Convergence
Date: 2008
Type: Thesis
Type: Masters
Type: MSc
Identifier: vital:5411
Identifier: http://hdl.handle.net/10962/d1005225
Identifier: Lattice theory
Identifier: Uniform spaces
Identifier: Convergence
Description: 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.
Format: 122 p,, pdf
Publisher: Rhodes University, Faculty of Science, Mathematics
Language: English
Rights: Craig, Andrew Philip Knott

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