Characterization of stratified L-topological spaces by convergence of stratified L-filters

Orpen, David Lisle (2010) Characterization of stratified L-topological spaces by convergence of stratified L-filters. Masters thesis, Rhodes University.

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Abstract

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.

Item Type:Thesis (Masters)
Uncontrolled Keywords:Topology, Generalized spaces, Filters (Mathematics), Topological spaces
Subjects:Q Science > QA Mathematics
Divisions:Faculty > Faculty of Science > Mathematics (Pure & Applied)
ID Code:2161
Deposited By: Ms Chantel Clack
Deposited On:07 Nov 2011 09:39
Last Modified:06 Jan 2012 16:22
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