- Title
- Characterization of stratified L-topological spaces by convergence of stratified L-filters
- Creator
- Orpen, David Lisle
- ThesisAdvisor
- Jager, Gunther
- Subject
- Topology
- Subject
- Generalized spaces
- Subject
- Filters (Mathematics)
- Subject
- Topological spaces
- Date
- 2011
- Type
- Thesis
- Type
- Masters
- Type
- MSc
- Identifier
- vital:5402
- Identifier
- http://hdl.handle.net/10962/d1005216
- Identifier
- Topology
- Identifier
- Generalized spaces
- Identifier
- Filters (Mathematics)
- Identifier
- Topological spaces
- Description
- For the case where L is an ecl-premonoid, we explore various characterizations of SL-topological spaces, in particular characterization in terms of a convergence function lim: FS L(X) ! LX. We find we have to introduce a new axiom , L on the lim function in order to completely describe SL-topological spaces, which is not required in the case where L is a frame. We generalize the classical Kowalski and Fischer axioms to the lattice context and examine their relationship to the convergence axioms. We define the category of stratified L-generalized convergence spaces, as a generalization of the classical convergence spaces and investigate conditions under which it contains the category of stratified L-topological spaces as a reflective subcategory. We investigate some subcategories of the category of stratified L-generalized convergence spaces obtained by generalizing various classical convergence axioms.
- Format
- 129 p., pdf
- Publisher
- Rhodes University, Faculty of Science, Mathematics
- Language
- English
- Rights
- Orpen, David Lisle
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Collections
RU Department of Mathematics (Pure and Applied)
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