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  • Characterizing Lie groups by controlling their zero-dimensional subgroups
    Dikranjan, Dikran N., 1950- ; Shakhmatov, Dmitri
    We provide characterizations of Lie groups as compact-like groups in which all closed zero-dimensional metric (compact) subgroups are discrete. The "compact-like" properties we consider include ... (local) compactness, (local) ▫$\omega$▫-boundedness, (local) countable compactness, (local) precompactness, (local) minimality and sequential completeness. A sample of our characterizations is as follows: (i) A topological group is a Lie group if and only if it is locally compact and has no infinite compact metric zero-dimensional subgroups. (ii) An abelian topological group ▫$G$▫ is a Lie group if and only if ▫$G$▫ is locally minimal, locally precompact and all closed metric zero-dimensional subgroups of ▫$G$▫ are discrete. (iii) An abelian topological group is a compact Lie group if and only if it is minimal and has no infinite closed metric zero-dimensional subgroups. (iv) An infinite topological group is a compact Lie group if and only if it is sequentially complete, precompact, locally minimal, contains a non-empty open connected subset and all its compact metric zero-dimensional subgroups are finite.
    Vir: Forum mathematicum. - ISSN 0933-7741 (Vol. 30, iss. 2, March 2018, str. 295-320)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2017
    Jezik - angleški
    COBISS.SI-ID - 18080857

    Povezava(-e):

    http://doi.org/10.1515/forum-2017-0010
    DOI

vir: Forum mathematicum. - ISSN 0933-7741 (Vol. 30, iss. 2, March 2018, str. 295-320)
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