Journal of Lie Theory

no. 3
On the Compact Space of Closed Subgroups of Locally Compact Groups
Journal of Lie Theory, Volume 24 (2014) no. 3, pp. 715-723
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.
DOI: 10.5802/jolt.803
Classification: 54B20, 22D05
Keywords: 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},
     doi = {10.5802/jolt.803},
     zbl = {1305.54020},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.803/}
}
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H. Hamrouni; B. Kadri. On the Compact Space of Closed Subgroups of Locally Compact Groups. Journal of Lie Theory, Volume 24 (2014) no. 3, pp. 715-723. doi: 10.5802/jolt.803

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