Geodesic
On the Compact Space of Closed Subgroups of Locally Compact Groups
Journal of Lie theory, Tome 24 (2014) no. 3, pp. 715-723 Cet article a éte moissonné depuis la source Heldermann Verlag

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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.
Classification : 54B20, 22D05
Mots-clés : Lie projective group, pro-Lie group, hyperspace, Chabauty topology, projective limit, strong projective limit, almost connected group 
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     author = {H. Hamrouni and B. Kadri},
     title = {On the {Compact} {Space} of {Closed} {Subgroups} of {Locally} {Compact} {Groups}},
     journal = {Journal of Lie theory},
     pages = {715--723},
     year = {2014},
     volume = {24},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JLT_2014_24_3_JLT_2014_24_3_a5/}
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H. Hamrouni; B. Kadri. On the Compact Space of Closed Subgroups of Locally Compact Groups. Journal of Lie theory, Tome 24 (2014) no. 3, pp. 715-723. http://geodesic.mathdoc.fr/item/JLT_2014_24_3_JLT_2014_24_3_a5/