HATEM HAMROUNI
Articles written in Proceedings – Mathematical Sciences
Volume 124 Issue 1 February 2014 pp 37-55
On Approximation of Lie Groups by Discrete Subgroups
A locally compact group 𝐺 is said to be approximated by discrete sub-groups (in the sense of Tôyama) if there is a sequence of discrete subgroups of 𝐺 that converges to 𝐺 in the Chabauty topology (or equivalently, in the Vietoris topology). The notion of approximation of Lie groups by discrete subgroups was introduced by Tôyama in
Volume 131 All articles Published: 19 February 2021 Article ID 0006 Article
A characterization of totally disconnected compactly ruled groups
A locally compact group $G$ is called compactly ruled if it is a directed union of compact open subgroups. We denote by $\mathcal{SUB}(G)$ the space of closed subgroups of $G$ equipped with the Chabauty topology. In this paper, we show that the subspace $\mathcal{SUB}_{\rm co} (G)$ of $\mathcal{SUB}(G)$ consisting of compact open subgroups is dense in $\mathcal{SUB}(G)$ if and only if $G$ is totally disconnected compactly ruled.
Volume 131, 2021
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