Characterization of stratified L-topological spaces by convergence of stratified L-filters
- Authors: Orpen, David Lisle
- Date: 2011
- Subjects: Topology , Generalized spaces , Filters (Mathematics) , Topological spaces
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5402 , http://hdl.handle.net/10962/d1005216 , Topology , Generalized spaces , Filters (Mathematics) , 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.
- Full Text:
- Date Issued: 2011
Generalisations of filters and uniform spaces
- Authors: Muraleetharan, Murugiah
- Date: 1997
- Subjects: Filters (Mathematics) , Uniform spaces
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5409 , http://hdl.handle.net/10962/d1005223 , Filters (Mathematics) , Uniform spaces
- Description: The notion of a filter F ∈ 2²x has been extended to that of a : prefilter: ƒ ∈ 1²x, generalised filter ƒ ∈ 2²x x and fuzzy filter ᵩ ∈ 1¹x. A uniformity is a filter with some other conditions and the notion of a uniformity D ∈ 2²xxx has been extended to that of a : fuzzy uniformity d ∈ 1²xxx , generalised uniformity ∈ 1²xxx and super uniformity b ∈ 1¹x. We establish categorical embeddings from the category of uniform spaces into the categories of fuzzy uniform spaces, generalised uniform spaces and super uniform spaces and also categorical embeddings into the category of super uniform spaces from the categories of fuzzy uniform spaces and generalised uniform spaces.
- Full Text:
- Date Issued: 1997