• A characterization of totally disconnected compactly ruled groups

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      https://www.ias.ac.in/article/fulltext/pmsc/131/0006

    • Keywords

       

      Totally disconnected locally compact group; compactly ruled; Chabauty topology.

    • Abstract

       

      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.

    • Author Affiliations

       

      HATEM HAMROUNI1 ZOUHOUR JLALI1

      1. Department of Mathematics, Faculty of Sciences at Sfax, Sfax University, B.P. 1171, 3000 Sfax, Tunisia
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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