Un estudio de las compactificaciones fibra a fibra
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Autores
Rocha Barriga, Juan Carlos
Director
Neira Uribe, Clara Marina
Tipo de contenido
Trabajo de grado - Maestría
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EspañolFecha de publicación
2013-12-10
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Resumen
Se estudia la extension de los meéodos de compactificación de Stone-Cech de la topología clásica al caso de la topología fibrada. En el primer capítulo se introducen los conceptos y resultados básicos de la topología fibrada. En el segundo capítulo se estudia el concepto de producto topológico parcial para después aplicarlo a la extensión del proceso de compactificación de Stone-Cech por medio de productos topológicos al ambito fibrado. También se muestran propiedades de universalidad de la compactificación obtenida. En el tercer capítulo se estudian las ideas de b-z-conjunto y b-z-filtro, para después aplicarlas a la extensión del método de compactificación clásica por medio de cero conjuntos y z-filtros, al caso de la topología fibrada. Se muestran también propiedades de universalidad asociadas a la compactificación obtenida. Se señala que en el caso fibrado aun es incierta la coincidencia de los dos métodos de compactificación.
Abstract. Extensions of the Stone-ˇ Cech compactification methods of classic topology to the case of fibrewise topology are studied. In the first chapter the basic ideas and results of fibrewise topology are introduced. In the second chapter the idea of partial topological product is studied and then applied to the extension to the fibrewise case of the Stone-ˇ Cech compactification method through topological products. Also, universal properties of the obtained compatification are exhibited. In the third chapter the ideas of b-z-set and b-z-filter are introduced, and then applied to the extension of the process of compatification through zero sets and z-filters to the case of fibrewise topology. Universal properties associated to the compatification obtained are shown. It is pointed out that in the fibrewise case, the equivalence of the two methods of compactification is not settled yet.
Abstract. Extensions of the Stone-ˇ Cech compactification methods of classic topology to the case of fibrewise topology are studied. In the first chapter the basic ideas and results of fibrewise topology are introduced. In the second chapter the idea of partial topological product is studied and then applied to the extension to the fibrewise case of the Stone-ˇ Cech compactification method through topological products. Also, universal properties of the obtained compatification are exhibited. In the third chapter the ideas of b-z-set and b-z-filter are introduced, and then applied to the extension of the process of compatification through zero sets and z-filters to the case of fibrewise topology. Universal properties associated to the compatification obtained are shown. It is pointed out that in the fibrewise case, the equivalence of the two methods of compactification is not settled yet.