Every group of totally disconnected type is locally profinite?












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Let $G$ be a Hausdorff topological group in which every point has a neighborhood basis of open compact neighborhoods. Let's call this a group of totally disconnected (td)-type.



On the other hand, we have a notion of a locally profinite group, a Hausdorff topological group which has a neighborhood basis of the identity consisting of open compact subgroups. A locally profinite group is obviously of td-tytpe.



Is there an example of a group of td-type which is not locally profinite?










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    Let $G$ be a Hausdorff topological group in which every point has a neighborhood basis of open compact neighborhoods. Let's call this a group of totally disconnected (td)-type.



    On the other hand, we have a notion of a locally profinite group, a Hausdorff topological group which has a neighborhood basis of the identity consisting of open compact subgroups. A locally profinite group is obviously of td-tytpe.



    Is there an example of a group of td-type which is not locally profinite?










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      3












      3








      3







      Let $G$ be a Hausdorff topological group in which every point has a neighborhood basis of open compact neighborhoods. Let's call this a group of totally disconnected (td)-type.



      On the other hand, we have a notion of a locally profinite group, a Hausdorff topological group which has a neighborhood basis of the identity consisting of open compact subgroups. A locally profinite group is obviously of td-tytpe.



      Is there an example of a group of td-type which is not locally profinite?










      share|cite|improve this question













      Let $G$ be a Hausdorff topological group in which every point has a neighborhood basis of open compact neighborhoods. Let's call this a group of totally disconnected (td)-type.



      On the other hand, we have a notion of a locally profinite group, a Hausdorff topological group which has a neighborhood basis of the identity consisting of open compact subgroups. A locally profinite group is obviously of td-tytpe.



      Is there an example of a group of td-type which is not locally profinite?







      topological-groups profinite-groups






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      asked Nov 12 '18 at 6:25









      D_S

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          "Is there an example of a group of td-type which is not locally profinite?"



          No. This was proved by D. van Dantzig in the 1930s:



          Van Dantzig, D.: Zur topologischen Algebra. III. Brouwersche und Cantorsche Gruppen, Compositio Mathematica, Volume 3 (1936), p. 408-426



          For a modern presentation of the proof, see e.g. Phillip Wesolek's lecture notes:
          http://people.math.binghamton.edu/wesolek/tdlc_Polish_groups/tdlcPolish.html






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            "Is there an example of a group of td-type which is not locally profinite?"



            No. This was proved by D. van Dantzig in the 1930s:



            Van Dantzig, D.: Zur topologischen Algebra. III. Brouwersche und Cantorsche Gruppen, Compositio Mathematica, Volume 3 (1936), p. 408-426



            For a modern presentation of the proof, see e.g. Phillip Wesolek's lecture notes:
            http://people.math.binghamton.edu/wesolek/tdlc_Polish_groups/tdlcPolish.html






            share|cite|improve this answer


























              5














              "Is there an example of a group of td-type which is not locally profinite?"



              No. This was proved by D. van Dantzig in the 1930s:



              Van Dantzig, D.: Zur topologischen Algebra. III. Brouwersche und Cantorsche Gruppen, Compositio Mathematica, Volume 3 (1936), p. 408-426



              For a modern presentation of the proof, see e.g. Phillip Wesolek's lecture notes:
              http://people.math.binghamton.edu/wesolek/tdlc_Polish_groups/tdlcPolish.html






              share|cite|improve this answer
























                5












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                "Is there an example of a group of td-type which is not locally profinite?"



                No. This was proved by D. van Dantzig in the 1930s:



                Van Dantzig, D.: Zur topologischen Algebra. III. Brouwersche und Cantorsche Gruppen, Compositio Mathematica, Volume 3 (1936), p. 408-426



                For a modern presentation of the proof, see e.g. Phillip Wesolek's lecture notes:
                http://people.math.binghamton.edu/wesolek/tdlc_Polish_groups/tdlcPolish.html






                share|cite|improve this answer












                "Is there an example of a group of td-type which is not locally profinite?"



                No. This was proved by D. van Dantzig in the 1930s:



                Van Dantzig, D.: Zur topologischen Algebra. III. Brouwersche und Cantorsche Gruppen, Compositio Mathematica, Volume 3 (1936), p. 408-426



                For a modern presentation of the proof, see e.g. Phillip Wesolek's lecture notes:
                http://people.math.binghamton.edu/wesolek/tdlc_Polish_groups/tdlcPolish.html







                share|cite|improve this answer












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                share|cite|improve this answer










                answered Nov 12 '18 at 7:06









                Colin Reid

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