Weak and strong topologies in topological abelian group
The main topic of this thesis are the weak and strong topologies on abelian groups. The former notion is generally known in the theory of topological abelian groups; the most common example is probably the celebrated Bohr topology. The latter notion is known mainly in the theory of topological vecto...
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|---|---|
| Formato: | tesis doctoral |
| Fecha de publicación: | 2009 |
| País: | España |
| Recursos: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/48610 |
| Acesso em linha: | https://hdl.handle.net/20.500.14352/48610 |
| Access Level: | acceso abierto |
| Palavra-chave: | 512.541(043.2) Grupos localmente cuasi-convexos Topología de Bohr Topología de Mackey Topological abelian group Weak and strong topologies Mackey topology Topología 1210 Topología |
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Weak and strong topologies in topological abelian groupLeo, Lorenzo de512.541(043.2)Grupos localmente cuasi-convexosTopología de BohrTopología de MackeyTopological abelian groupWeak and strong topologiesMackey topologyTopología1210 TopologíaThe main topic of this thesis are the weak and strong topologies on abelian groups. The former notion is generally known in the theory of topological abelian groups; the most common example is probably the celebrated Bohr topology. The latter notion is known mainly in the theory of topological vector spaces, as the equally celebrated Mackey topology. This is why, the origin of a “global” study of weak and strong topologies is deeply rooted in the theory of topological vector spaces, where similar notions appeared for the first time (see § for details). A starting step in the foundation of this kind of study in the framework of topological abelian group was done by Chasco, Mart´ın Peinador and Tarieladze in [23]. In this paper, they show — among other results — that it is natural to restrict to the class of locally quasi-convex groups. Such a class of groups is widely known and used in different instances, but we observed that there is a deep lack of knowledge of the quasi-convex subsets, even in thoroughly studied groups like, for example, the integers or the unitary complex circle. The main aim of the present thesis is to offer a contribution to the study begun in [23]. This is done by introducing new notions and proving new results that permit to widen the knowledge on the weak and strong topologies in locally quasi-convex groups. In order to develop this line we need a solid background on the Bohr topology and the theory of the quasi-convex subsets of a topological group. The first part of the thesis is dedicated to this trend.Universidad Complutense de Madrid, Servicio de PublicacionesMartín Peinador, ElenaDikranjan, Dikran N.Universidad Complutense de Madrid20092009-01-2920092009-01-29doctoral thesishttp://purl.org/coar/resource_type/c_db06info:eu-repo/semantics/doctoralThesisapplication/pdfhttps://hdl.handle.net/20.500.14352/48610reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/486102026-06-02T12:44:21Z |
| dc.title.none.fl_str_mv |
Weak and strong topologies in topological abelian group |
| title |
Weak and strong topologies in topological abelian group |
| spellingShingle |
Weak and strong topologies in topological abelian group Leo, Lorenzo de 512.541(043.2) Grupos localmente cuasi-convexos Topología de Bohr Topología de Mackey Topological abelian group Weak and strong topologies Mackey topology Topología 1210 Topología |
| title_short |
Weak and strong topologies in topological abelian group |
| title_full |
Weak and strong topologies in topological abelian group |
| title_fullStr |
Weak and strong topologies in topological abelian group |
| title_full_unstemmed |
Weak and strong topologies in topological abelian group |
| title_sort |
Weak and strong topologies in topological abelian group |
| dc.creator.none.fl_str_mv |
Leo, Lorenzo de |
| author |
Leo, Lorenzo de |
| author_facet |
Leo, Lorenzo de |
| author_role |
author |
| dc.contributor.none.fl_str_mv |
Martín Peinador, Elena Dikranjan, Dikran N. Universidad Complutense de Madrid |
| dc.subject.none.fl_str_mv |
512.541(043.2) Grupos localmente cuasi-convexos Topología de Bohr Topología de Mackey Topological abelian group Weak and strong topologies Mackey topology Topología 1210 Topología |
| topic |
512.541(043.2) Grupos localmente cuasi-convexos Topología de Bohr Topología de Mackey Topological abelian group Weak and strong topologies Mackey topology Topología 1210 Topología |
| description |
The main topic of this thesis are the weak and strong topologies on abelian groups. The former notion is generally known in the theory of topological abelian groups; the most common example is probably the celebrated Bohr topology. The latter notion is known mainly in the theory of topological vector spaces, as the equally celebrated Mackey topology. This is why, the origin of a “global” study of weak and strong topologies is deeply rooted in the theory of topological vector spaces, where similar notions appeared for the first time (see § for details). A starting step in the foundation of this kind of study in the framework of topological abelian group was done by Chasco, Mart´ın Peinador and Tarieladze in [23]. In this paper, they show — among other results — that it is natural to restrict to the class of locally quasi-convex groups. Such a class of groups is widely known and used in different instances, but we observed that there is a deep lack of knowledge of the quasi-convex subsets, even in thoroughly studied groups like, for example, the integers or the unitary complex circle. The main aim of the present thesis is to offer a contribution to the study begun in [23]. This is done by introducing new notions and proving new results that permit to widen the knowledge on the weak and strong topologies in locally quasi-convex groups. In order to develop this line we need a solid background on the Bohr topology and the theory of the quasi-convex subsets of a topological group. The first part of the thesis is dedicated to this trend. |
| publishDate |
2009 |
| dc.date.none.fl_str_mv |
2009 2009-01-29 2009 2009-01-29 |
| dc.type.none.fl_str_mv |
doctoral thesis http://purl.org/coar/resource_type/c_db06 |
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info:eu-repo/semantics/doctoralThesis |
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doctoralThesis |
| dc.identifier.none.fl_str_mv |
https://hdl.handle.net/20.500.14352/48610 |
| url |
https://hdl.handle.net/20.500.14352/48610 |
| dc.language.none.fl_str_mv |
Inglés eng |
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Inglés |
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eng |
| dc.rights.none.fl_str_mv |
open access http://purl.org/coar/access_right/c_abf2 |
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info:eu-repo/semantics/openAccess |
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open access http://purl.org/coar/access_right/c_abf2 |
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openAccess |
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application/pdf |
| dc.publisher.none.fl_str_mv |
Universidad Complutense de Madrid, Servicio de Publicaciones |
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Universidad Complutense de Madrid, Servicio de Publicaciones |
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reponame:Docta Complutense instname:Universidad Complutense de Madrid (UCM) |
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Universidad Complutense de Madrid (UCM) |
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Docta Complutense |
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Docta Complutense |
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15,301603 |