Almost periodic compactifications of group extensions

Junghenn, H. D. ; Milnes, P.

Czechoslovak Mathematical Journal, Tome 52 (2002) no. 2, pp. 237-254.

Résumé

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 $G$.

Détail

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