Journal of Lie Theory

no. 1
On the Continuity of the Centralizer Map of a Locally Compact Group
Journal of Lie Theory, Volume 26 (2016) no. 1, pp. 117-134
\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 $G$.
DOI: 10.5802/jolt.883
Classification: 22D05, 22O05, 54B20
Keywords: Locally compact group, profinite group, quasidiscrete group, Frattini subgroup, one-parameter subgroup, Chabauty topology 
@article{JOLT_2016_26_1_a5,
     author = {H. Hamrouni and F. Sadki},
     title = {On the {Continuity} of the {Centralizer} {Map} of a {Locally} {Compact} {Group}},
     journal = {Journal of Lie Theory},
     pages = {117--134},
     year = {2016},
     volume = {26},
     number = {1},
     doi = {10.5802/jolt.883},
     zbl = {1348.22008},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.883/}
}
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H. Hamrouni; F. Sadki. On the Continuity of the Centralizer Map of a Locally Compact Group. Journal of Lie Theory, Volume 26 (2016) no. 1, pp. 117-134. doi: 10.5802/jolt.883

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