Craig, A.P.K. (2008) Lattice-valued uniform convergence spaces : the case of enriched lattices. Masters thesis, Rhodes University.
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.)|
|Deposited By:||Rhodes Library Archive Administrator|
|Deposited On:||10 Mar 2009|
|Last Modified:||06 Jan 2012 16:20|
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