Bockstein theorem for nilpotent groups
| Autor: | Cencelj, M., Dydak, J., Mitra, A., Vavpetic, A. |
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| Rok vydání: | 2008 |
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| Zdroj: | Proceedings of the American Math.Soc. 138 (2010), 1501-1510 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1090/S0002-9939-09-10143-0 |
| Popis: | We extend the definition of Bockstein basis $\sigma(G)$ to nilpotent groups $G$. A metrizable space $X$ is called a {\it Bockstein space} if $\dim_G(X) = \sup\{\dim_H(X) | H\in \sigma(G)\}$ for all Abelian groups $G$. Bockstein First Theorem says that all compact spaces are Bockstein spaces. Here are the main results of the paper: Let $X$ be a Bockstein space. If $G$ is nilpotent, then $\dim_G(X) \leq 1$ if and only if $\sup\{\dim_H(X) | H\in\sigma(G)\}\leq 1$. $X$ is a Bockstein space if and only if $\dim_{\Z_{(l)}} (X) = \dim_{\hat{Z}_{(l)}}(X)$ for all subsets $l$ of prime numbers. Comment: 10 pages |
| Databáze: | arXiv |
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