Bourbaki-complete spaces and Samuel realcompactification
This thesis belongs to the area of General Topology and, in particular, to the field of study of uniform spaces. It is divided in three parts where the related topics Bourbaki-completeness and Samuel realcompactification are studied. Many of the results presented here have already been published by...
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| Tipo de recurso: | tesis doctoral |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/17301 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/17301 |
| Access Level: | acceso abierto |
| Palabra clave: | 515.123(043.2) Espacios uniformes Uniform Spaces Matemáticas (Matemáticas) 12 Matemáticas |
| Sumario: | This thesis belongs to the area of General Topology and, in particular, to the field of study of uniform spaces. It is divided in three parts where the related topics Bourbaki-completeness and Samuel realcompactification are studied. Many of the results presented here have already been published by the author in the following papers. [GaMe14] M. I. Garrido and A. S. Mero~no, New types of completeness in metric spaces, Ann. Acad. Sci. Fenn. Math. 39 (2014) 733-758. [GaMe16] M. I. Garrido and A. S. Mero~no, On paracompactness, completeness and boundedness in uniform spaces, Topology Appl. 203 (2016)98-107. [GaMe17] M. I. Garrido and A. S. Mero~no, The Samuel realcompactification of a metric space, J. Math. Anal. Appl. 456 (2017) 1013-1039. [GaMe18] M. I. Garrido and A. S. Mero~no, The Samuel realcompactification,Topology Appl. 241 (2018) 150-161. [HoJuMe19] A. Hohti, H. Junnila and A. S Mero~no, On strongly Cechcomplete spaces, to appear in Topology Appl. (2019). In addition, new results, originated during the writing process, have been included. In the first part of the thesis we present many results of [GaMe14], [GaMe16] and some of [HoJuMe19]. More precisely, we study Bourbaki-completeness and cofinal Bourbaki-completeness (equivalently uniform strong-paracompactness) of uniform spaces. In particular, we solve several primary problems related to products, subspaces, hyperspaces, metric spaces and fine spaces... |
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