Espaços Vetoriais Topológicos

• Autor(a) principal: Cavalcante, Wasthenny Vasconcelos
• Data de Publicação: 2015
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da UFPB
• Texto Completo: https://repositorio.ufpb.br/jspui/handle/tede/9277
• topic: Espaços Vetoriais Topológicos; Espaços Localmente Convexos; Topologias; Teorema de Hahn-Banach; Teorema de Banach-Alaoglu; Teorema de Banach- Steinhauss; Teorema da Aplicação Aberta; Teorema do Gráfico Fechado; Topological vector spaces; Locally convex spaces; Topologies; Hahn-Banach Theorem; Theorem of Banach-Alaoglu; Theorem of Banach-Steinhauss; Open Mapping Theorem; Closed Graph Theorem; CIENCIAS EXATAS E DA TERRA::MATEMATICA

In this work we investigate the concept of topological vector spaces and their properties. In the rst chapter we present two sections of basic results and in the other sections we present a more general study of such spaces. In the second chapter we restrict ourselves to the real scalar eld and we study, in the context of locally convex spaces, the Hahn-Banach and Banach-Alaoglu theorems. We also build the weak, weak-star, of bounded convergence and of pointwise convergence topologies. Finally we investigate the Theorem of Banach-Steinhauss, the Open Mapping Theorem and the Closed Graph Theorem.