Orpen, David Lisle (2010) Characterization of stratified Ltopological spaces by convergence of stratified Lfilters. Masters thesis, Rhodes University.

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Abstract
For the case where L is an eclpremonoid, we explore various characterizations of SLtopological 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 SLtopological 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 Lgeneralized convergence spaces, as a generalization of the classical convergence spaces and investigate conditions under which it contains the category of stratified Ltopological spaces as a reflective subcategory. We investigate some subcategories of the category of stratified Lgeneralized 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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