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

Craig, A.P.K. (2008) Lattice-valued uniform convergence spaces : the case of enriched lattices. Masters thesis, Rhodes University.

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Abstract

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.

Item Type:Thesis (Masters)
Additional Information:M.Sc. (Mathematics)
Uncontrolled Keywords:Lattice theory, uniform spaces, uniform convergence spaces, lattice-valued spaces, category theory
Subjects:Y Unknown > Subjects to be assigned
Divisions:Faculty > Faculty of Science > Mathematics (Pure & Applied)
Supervisors:Jäger, G. (Prof.)
ID Code:1304
Deposited By: Rhodes Library Archive Administrator
Deposited On:10 Mar 2009
Last Modified:06 Jan 2012 16:20
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