Repositório Digital

metadata.rede.dc.title:	On the Banach-Stone theorem and the manifold topological classification
metadata.rede.dc.contributor.author:	Botelho, Luiz C. L.
metadata.rede.dc.publisher:	Centro Brasileiro de Pesquisas Físicas
metadata.rede.dc.date.issued:	2009
metadata.rede.dc.description.resumo:	We present a simple set-theoretic proof of the Banach-Stone Theorem. We thus apply this Topological Classification theorem to the still-unsolved problem of topological classification of Euclidean Manifolds through two conjectures and additionaly we give a straightforward proof of the famous Brower theorem for manifolds topologically classified by their Euclidean dimensions. \noindent We start our comment announcing the:\noindent{\bf Banach-Stone Theorem} ([1]). Let $X$ and $Y$ be compact Hausdorff spaces, such that the associated function algebras of continuous functions $C(X,R)$ and $C(Y,R)$ separate points in $X$ and $Y$ respectively. We have thus \noindent a)\quad $X$ and $Y$ are homeomorphic $\Leftrightarrow$ \noindent b)\quad $C(X,R)$ and $C(Y,R)$ are isomorphic.
metadata.rede.dc.identifier.uri:	https://repositorio.mcti.gov.br/handle/mctic/6558
Appears in Collections:	Publicações CBPF

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