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
- 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
Extension theorems on L-topological spaces and L-fuzzy vector spaces
- Authors: Pinchuck, Andrew
- Date: 2002
- Subjects: Topology , Vector spaces , Generalized spaces
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5405 , http://hdl.handle.net/10962/d1005219 , Topology , Vector spaces , Generalized spaces
- Description: A non-trivial example of an L-topological space, the fuzzy real line is examined. Various L-topological properties and their relationships are developed. Extension theorems on the L-fuzzy real line as well as extension theorems on more general L-topological spaces follow. Finally, a theory of L-fuzzy vector spaces leads up to a fuzzy version of the Hahn-Banach theorem.
- Full Text:
- Date Issued: 2002
- Authors: Pinchuck, Andrew
- Date: 2002
- Subjects: Topology , Vector spaces , Generalized spaces
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5405 , http://hdl.handle.net/10962/d1005219 , Topology , Vector spaces , Generalized spaces
- Description: A non-trivial example of an L-topological space, the fuzzy real line is examined. Various L-topological properties and their relationships are developed. Extension theorems on the L-fuzzy real line as well as extension theorems on more general L-topological spaces follow. Finally, a theory of L-fuzzy vector spaces leads up to a fuzzy version of the Hahn-Banach theorem.
- Full Text:
- Date Issued: 2002
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