Journal of Lie Theory 26 (2016), No. 1, 117--134
Copyright Heldermann Verlag 2016
On the Continuity of the Centralizer Map of a Locally Compact Group
Hatem Hamrouni
Dept. of Mathematics, Faculty of Sciences, Sfax University, B. P. 1171, 3000 Sfax, Tunisia
hatemhhamrouni@voila.fr
Firas Sadki
Dept. of Mathematics, Faculty of Sciences, Sfax University, B. P. 1171, 3000 Sfax, Tunisia
[Abstract-pdf]
\def\ch{{\cal S\hskip-.5pt U\hskip-.9pt B}} Let $G$ be a locally compact group. We denote by $\ch(G)$ the hyperspace of closed subgroups of $G$ endowed with the Chabauty topology. In this article we study the continuity of the map centr$\colon G\to\ch(G)$, $g \mapsto{\rm centr}(g)$, where centr$(g)$ is the centralizer of $g$ in $G$.
Keywords: Locally compact group, profinite group, quasidiscrete group, Frattini subgroup, one-parameter subgroup, Chabauty topology.
MSC: 22D05, 22O05, 54B20
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