Nota de FísicaPublicado
On the Banach-Stone Theorem and the Manifold Topological Classification
Dados da publicação
- Autores
- —
- Tipo
- Nota de Física
- Status
- Publicado
- Data de publicação
- 01/07/2009
- Descrição
- 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.
- Ano
- 2009
- Vínculo com tese
- Não
- Vínculo com bolsa
- Não