Lattice-valued uniform convergence spaces the case of enriched lattices
- Authors: Craig, Andrew Philip Knott
- Date: 2008
- Subjects: Lattice theory , Uniform spaces , Convergence
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5411 , http://hdl.handle.net/10962/d1005225 , Lattice theory , Uniform spaces , Convergence
- Description: Using a pseudo-bisymmetric enriched cl-premonoid as the underlying lattice, we examine different categories of lattice-valued spaces. Lattice-valued topological spaces, uniform spaces and limit spaces are described, and we produce a new definition of stratified lattice-valued uniform convergence spaces in this generalised lattice context. We show that the category of stratified L-uniform convergence spaces is topological, and that the forgetful functor preserves initial constructions for the underlying stratified L-limit space. For the case of L a complete Heyting algebra, it is shown that the category of stratified L-uniform convergence spaces is cartesian closed.
- Full Text:
- Date Issued: 2008
- Authors: Craig, Andrew Philip Knott
- Date: 2008
- Subjects: Lattice theory , Uniform spaces , Convergence
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5411 , http://hdl.handle.net/10962/d1005225 , Lattice theory , Uniform spaces , Convergence
- Description: Using a pseudo-bisymmetric enriched cl-premonoid as the underlying lattice, we examine different categories of lattice-valued spaces. Lattice-valued topological spaces, uniform spaces and limit spaces are described, and we produce a new definition of stratified lattice-valued uniform convergence spaces in this generalised lattice context. We show that the category of stratified L-uniform convergence spaces is topological, and that the forgetful functor preserves initial constructions for the underlying stratified L-limit space. For the case of L a complete Heyting algebra, it is shown that the category of stratified L-uniform convergence spaces is cartesian closed.
- Full Text:
- Date Issued: 2008
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
- 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
Complete regularity and related concepts in L-uniform spaces
- Authors: Harnett, Rait Sicklen
- Date: 1992
- Subjects: Uniform spaces , Mathematics -- Research
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5403 , http://hdl.handle.net/10962/d1005217 , Uniform spaces , Mathematics -- Research
- Description: L will denote a completely distributive lattice with an order reversing involution. The concept of an L-uniform space is introduced. An extension theorem concerning L-uniformly continuous functions is proved. A characterisation of L-uniformizability, involving L-complete regularity is given. With respect to L--completely regular spaces it is shown that the topological modification of an L-completely regular space is completely regular. Furthermore it is shown that the topologically generated L-topology of a completely regular space is L-completely regular.
- Full Text:
- Date Issued: 1992
- Authors: Harnett, Rait Sicklen
- Date: 1992
- Subjects: Uniform spaces , Mathematics -- Research
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5403 , http://hdl.handle.net/10962/d1005217 , Uniform spaces , Mathematics -- Research
- Description: L will denote a completely distributive lattice with an order reversing involution. The concept of an L-uniform space is introduced. An extension theorem concerning L-uniformly continuous functions is proved. A characterisation of L-uniformizability, involving L-complete regularity is given. With respect to L--completely regular spaces it is shown that the topological modification of an L-completely regular space is completely regular. Furthermore it is shown that the topologically generated L-topology of a completely regular space is L-completely regular.
- Full Text:
- Date Issued: 1992
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