Compactification of lattice-valued convergence spaces
- Authors: Jäger, Gunter
- Date: 2010
- Language: English
- Type: text , Article
- Identifier: vital:6828 , http://hdl.handle.net/10962/d1012339
- Description: We define compactness for stratified lattice-valued convergence spaces and show that a Tychonoff theorem is true. Further a generalization of the classical Richardson compactification is given. This compactification has a universal property.
- Full Text:
- Date Issued: 2010
- Authors: Jäger, Gunter
- Date: 2010
- Language: English
- Type: text , Article
- Identifier: vital:6828 , http://hdl.handle.net/10962/d1012339
- Description: We define compactness for stratified lattice-valued convergence spaces and show that a Tychonoff theorem is true. Further a generalization of the classical Richardson compactification is given. This compactification has a universal property.
- Full Text:
- Date Issued: 2010
A common framework for lattice-valued uniform spaces and probabilistic uniform limit spaces
- Craig, Andrew P K, Jäger, Gunter
- Authors: Craig, Andrew P K , Jäger, Gunter
- Date: 2009
- Language: English
- Type: Article
- Identifier: vital:6784 , http://hdl.handle.net/10962/d1006927
- Description: We study a category of lattice-valued uniform convergence spaces where the lattice is enriched by two algebraic operations. This general setting allows us to view the category of lattice-valued uniform spaces as a reflective subcategory of our category, and the category of probabilistic uniform limit spaces as a coreflective subcategory.
- Full Text:
- Date Issued: 2009
- Authors: Craig, Andrew P K , Jäger, Gunter
- Date: 2009
- Language: English
- Type: Article
- Identifier: vital:6784 , http://hdl.handle.net/10962/d1006927
- Description: We study a category of lattice-valued uniform convergence spaces where the lattice is enriched by two algebraic operations. This general setting allows us to view the category of lattice-valued uniform spaces as a reflective subcategory of our category, and the category of probabilistic uniform limit spaces as a coreflective subcategory.
- Full Text:
- Date Issued: 2009
Lattice-valued convergence spaces and regularity
- Authors: Jäger, Gunter
- Date: 2008
- Language: English
- Type: text , Article
- Identifier: vital:6826 , http://hdl.handle.net/10962/d1012336
- Description: We define a regularity axiom for lattice-valued convergence spaces where the lattice is a complete Heyting algebra. To this end, we generalize the characterization of regularity by a ”dual form” of a diagonal condition. We show that our axiom ensures that a regular T1-space is separated and that regularity is preserved under initial constructions. Further we present an extension theorem for a continuous mapping from a subspace to a regular space. A characterization in the restricted case that the lattice is a complete Boolean algebra in terms of the closure of an L-filter is given.
- Full Text:
- Date Issued: 2008
- Authors: Jäger, Gunter
- Date: 2008
- Language: English
- Type: text , Article
- Identifier: vital:6826 , http://hdl.handle.net/10962/d1012336
- Description: We define a regularity axiom for lattice-valued convergence spaces where the lattice is a complete Heyting algebra. To this end, we generalize the characterization of regularity by a ”dual form” of a diagonal condition. We show that our axiom ensures that a regular T1-space is separated and that regularity is preserved under initial constructions. Further we present an extension theorem for a continuous mapping from a subspace to a regular space. A characterization in the restricted case that the lattice is a complete Boolean algebra in terms of the closure of an L-filter is given.
- Full Text:
- Date Issued: 2008
Pretopological and topological lattice-valued convergence spaces
- Authors: Jäger, Gunter
- Date: 2007
- Language: English
- Type: text , Article
- Identifier: vital:6827 , http://hdl.handle.net/10962/d1012337
- Description: We show that the classical axiom which characterizes pretopological convergence spaces splits into two axioms in the general Heyting algebra-valued case. Furthermore we present a generalization of Kowalski’s diagonal condition to the lattice-valued case.
- Full Text:
- Date Issued: 2007
- Authors: Jäger, Gunter
- Date: 2007
- Language: English
- Type: text , Article
- Identifier: vital:6827 , http://hdl.handle.net/10962/d1012337
- Description: We show that the classical axiom which characterizes pretopological convergence spaces splits into two axioms in the general Heyting algebra-valued case. Furthermore we present a generalization of Kowalski’s diagonal condition to the lattice-valued case.
- Full Text:
- Date Issued: 2007
Lattice-valued continuous convergence is induced by a lattice-valued uniform convergence structure
- Authors: Jäger, Gunter
- Date: 2006
- Language: English
- Type: text , Article
- Identifier: vital:6824 , http://hdl.handle.net/10962/d1012332
- Description: We define a stratified L-uniform convergence structure on the set of all continuous mappings from a stratified L-limit space to a stratified L-uniform convergence space. This structure induces L-continuous convergence. This shows that the category of all L-limit-uniformizable spaces is cartesian closed.
- Full Text:
- Date Issued: 2006
- Authors: Jäger, Gunter
- Date: 2006
- Language: English
- Type: text , Article
- Identifier: vital:6824 , http://hdl.handle.net/10962/d1012332
- Description: We define a stratified L-uniform convergence structure on the set of all continuous mappings from a stratified L-limit space to a stratified L-uniform convergence space. This structure induces L-continuous convergence. This shows that the category of all L-limit-uniformizable spaces is cartesian closed.
- Full Text:
- Date Issued: 2006
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