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• W2024524460 abstract "A topological group is minimal if it does not admit a strictly coarser Hausdorff group topology. The Roelcke uniformity (or lower uniformity) on a topological group is the greatest lower bound of the left and right uniformities. A group is Roelcke-precompact if it is precompact with respect to the Roelcke uniformity. Many naturally arising non-Abelian topological groups are Roelcke-precompact and hence have a natural compactification. We use such compactifications to prove that some groups of isometries are minimal. In particular, if U_1 is the Urysohn universal metric space of diameter 1, the group Iso(U_1) of all self-isometries of U_1 is Roelcke-precompact, topologically simple and minimal. We also show that every topological group is a subgroup of a minimal topologically simple Roelcke-precompact group of the form Iso(M), where M is an appropriate non-separable version of the Urysohn space." @default.
• W2024524460 created "2016-06-24" @default.
• W2024524460 creator A5005182172 @default.
• W2024524460 date "2008-08-01" @default.
• W2024524460 modified "2023-09-26" @default.
• W2024524460 title "On subgroups of minimal topological groups" @default.
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• W2024524460 doi "https://doi.org/10.1016/j.topol.2008.03.001" @default.
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