- 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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