Curvas de Peano, lineabilidade, espaçabilidade e algebrabilidade

• Ano de defesa: 2018
• Autor(a) principal: Santos Filho, Sérgio Roméro Vital dos
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal da Paraíba; Brasil; Matemática; Programa de Pós-Graduação em Matemática; UFPB
• Palavras-chave em Português: Lineabilidade; Espaçabilidade; Algebrabilidade; Curvas de Peano; Lineability; Spaceability; Algebrability; Peano curves; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://repositorio.ufpb.br/jspui/handle/123456789/14968

In this dissertation, we turn our attention to the space of the continuous surjections between euclidean spaces. We constructed a Peano curve, also known as a space ll curve, and proved a result of optimal lineability from the point of view of dimension. Then we prove some properties on the order of growth of whole functions and we deal with the problem of algebrability, proving that the space of continuous surjections with complex values is strongly maximal algebrable. Subsequently, we prove the spaceability of the Peano curves between euclidean spaces andwe nalize our work by bringing some generalizations of the presented results to topological vector spaces that are continuous image of the real line.