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.
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- 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.
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Sobriety of crisp and fuzzy topological spaces
- Authors: Jacot-Guillarmod, Paul
- Date: 2004
- Subjects: Topological spaces , Fuzzy sets
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5414 , http://hdl.handle.net/10962/d1005228 , Topological spaces , Fuzzy sets
- Description: The objective of this thesis is a survey of crisp and fuzzy sober topological spaces. We begin by examining sobriety of crisp topological spaces. We then extend this to the L- topological case and obtain analogous results and characterizations to those of the crisp case. We then brie y examine semi-sobriety of (L;M)-topological spaces.
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- Authors: Jacot-Guillarmod, Paul
- Date: 2004
- Subjects: Topological spaces , Fuzzy sets
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5414 , http://hdl.handle.net/10962/d1005228 , Topological spaces , Fuzzy sets
- Description: The objective of this thesis is a survey of crisp and fuzzy sober topological spaces. We begin by examining sobriety of crisp topological spaces. We then extend this to the L- topological case and obtain analogous results and characterizations to those of the crisp case. We then brie y examine semi-sobriety of (L;M)-topological spaces.
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(L, M)-fuzzy topological spaces
- Authors: Matutu, Phethiwe Precious
- Date: 1992
- Subjects: Topological spaces , Fuzzy sets
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5410 , http://hdl.handle.net/10962/d1005224 , Topological spaces , Fuzzy sets
- Description: The objective of this thesis is to develop certain aspects of the theory of (L,M)-fuzzy topological spaces, where L and M are complete lattices (with additional conditions when necessary). We obtain results which are to a large extent analogous to results given in a series of papers of Šostak (where L = M = [0,1]) but not necessarily with analogous proofs. Often, our generalizations require a variety of techniques from lattice theory e.g. from continuity or complete distributive lattices.
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- Authors: Matutu, Phethiwe Precious
- Date: 1992
- Subjects: Topological spaces , Fuzzy sets
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5410 , http://hdl.handle.net/10962/d1005224 , Topological spaces , Fuzzy sets
- Description: The objective of this thesis is to develop certain aspects of the theory of (L,M)-fuzzy topological spaces, where L and M are complete lattices (with additional conditions when necessary). We obtain results which are to a large extent analogous to results given in a series of papers of Šostak (where L = M = [0,1]) but not necessarily with analogous proofs. Often, our generalizations require a variety of techniques from lattice theory e.g. from continuity or complete distributive lattices.
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