Espaços de convergência e aplicações
Nenhuma Miniatura disponível
Data
2025-03-25
Autores
Perim, João Marcos Falcão
Título da Revista
ISSN da Revista
Título de Volume
Editor
Universidade Federal do Espírito Santo
Resumo
This dissertation investigates the theory of convergence spaces as an alter native approach to studying topological and analytical properties. In contrast to the classical approach based on neighborhoods and open sets, convergence spaces use filters and nets to define limits, offering a more flexible structure compatible with Functional Analysis and Algebraic Topology. The work pre sents a review of General Topology, exploring the transition from filters to nets, and discusses relevant applications, including the Arzel`a-Ascoli theorem and the construction of the fundamental group for limit spaces. In doing so, it aims to consolidate the importance of convergence spaces as a theoretical and practical tool for various areas of Mathematics
Descrição
Palavras-chave
Espaços topológicos , Espaços de convergência , Filtros , Redes , Análise funcional , Topologia , Algébrica , Topological spaces , Convergence spaces , Filters , Nets , Functional analysis , Algebraic topology