Geodesic
Almost periodic compactifications of group extensions
Czechoslovak Mathematical Journal, Tome 52 (2002) no. 2, pp. 237-254 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Let $N$ and $K$ be groups and let $G$ be an extension of $N$ by $K$. Given a property $\mathcal P$ of group compactifications, one can ask whether there exist compactifications $N^{\prime }$ and $K^{\prime }$ of $N$ and $K$ such that the universal $\mathcal P$-compactification of $G$ is canonically isomorphic to an extension of $N^{\prime }$ by $K^{\prime }$. We prove a theorem which gives necessary and sufficient conditions for this to occur for general properties $\mathcal P$ and then apply this result to the almost periodic and weakly almost periodic compactifications of $G$.
Let $N$ and $K$ be groups and let $G$ be an extension of $N$ by $K$. Given a property $\mathcal P$ of group compactifications, one can ask whether there exist compactifications $N^{\prime }$ and $K^{\prime }$ of $N$ and $K$ such that the universal $\mathcal P$-compactification of $G$ is canonically isomorphic to an extension of $N^{\prime }$ by $K^{\prime }$. We prove a theorem which gives necessary and sufficient conditions for this to occur for general properties $\mathcal P$ and then apply this result to the almost periodic and weakly almost periodic compactifications of $G$.
Classification : 22A20, 22D05, 43A60
Keywords: group extension; semidirect product; topological group; semitopological semigroup; right topological semigroup; compactification; almost periodic; weakly almost periodic; strongly almost periodic 
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Junghenn, H. D.; Milnes, P. Almost periodic compactifications of group extensions. Czechoslovak Mathematical Journal, Tome 52 (2002) no. 2, pp. 237-254. http://geodesic.mathdoc.fr/item/CMJ_2002_52_2_a1/

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