O Teorema de Stone-Weierstrass e aplicações

• Autor(a) principal: Lopes, Wanda Aparecida
• Data de Publicação: 2009
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFU
• Texto Completo: https://repositorio.ufu.br/handle/123456789/16772
• topic: Aproximação; Funções contínuas; Funções infinitamente diferenciáveis; Espaços compactos; Espaços separáveis; Espaços metrizáveis; Análise funcional; Teoria da aproximação; Approximation; Continuous functions; Infinitely differentiable functions; Compact spaces; Metrizable spaces; Separable spaces; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA

The aim of this dissertation is to prove and apply the Weierstrass Approximation Theo- rem, on the approximation of continuous functions on bounded closed intervals by polyno- mials, and the Stone-Weierstrass Theorem, on the approximation of continuous functions on compact topological spaces. As applications of the Weierstrass Approximation Theo- rem we deal with the momentum problem for continuous functions and the approximation of continuous functions on the line by in¯nitely di®erentiable functions. As applications of the Stone-Weierstrass Theorem we prove that the space C(K) of continuous functions on the compact K is separable if and only if K is metrizable and the existence of a com- pact space K such that C(K) is isometrically isomorphic to the space `1 of bounded sequences.