Journal of Lie Theory 24 (2014), No. 3, 715--723
Copyright Heldermann Verlag 2014
On the Compact Space of Closed Subgroups of Locally Compact Groups
Hatem Hamrouni
Department of Mathematics, Faculty of Sciences, Sfax University, B.P. 1171, 3000 Sfax, Tunisia
hatemhhamrouni@voila.fr
Bilel Kadri
Department of Mathematics, Faculty of Sciences, Sfax University, B.P. 1171, 3000 Sfax, Tunisia
bilel.kadri@yahoo.fr
Let G be a locally compact topological group. We denote by C(G) the hyperspace of all closed subgroups of G equipped with the Chabauty topology; this is a compact space. The main result of this paper is to prove that the assignment C: G -> C(G), is functorial from the category of locally compact groups and proper morphisms to the category of compact spaces and preserves projective limits of projective systems of topological groups in which all bonding maps are surjective and proper.
Keywords: Lie projective group, pro-Lie group, hyperspace, Chabauty topology, projective limit, strong projective limit, almost connected group.
MSC: 54B20, 22D05
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