On the Banach-Stone theorem and the manifold topological classification

Please use this identifier to cite or link to this item: https://repositorio.mcti.gov.br/handle/mctic/6558

Full metadata record

DC Field	Value	Language
dc.contributor.author	Botelho, Luiz C. L.	-
dc.date.accessioned	2024-08-23T21:06:04Z	-
dc.date.available	2024-08-23T21:06:04Z	-
dc.date.issued	2009	-
dc.identifier.uri	https://repositorio.mcti.gov.br/handle/mctic/6558	-
dc.language	en	pt_BR
dc.publisher	Centro Brasileiro de Pesquisas Físicas	pt_BR
dc.rights	Acesso Aberto	pt_BR
dc.title	On the Banach-Stone theorem and the manifold topological classification	pt_BR
dc.type	Folheto	pt_BR
dc.publisher.country	Brasil	pt_BR
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.	pt_BR
Appears in Collections:	Publicações CBPF

Files in This Item:

File	Description	Size	Format
2009_on_the_banach_stone_theorem_and_the_manifold.pdf		66.92 kB	Adobe PDF	View/Open

Opções de acessibilidade