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  • Locally compact abelian groups admitting non-trivial quasi-convex null sequences
    Dikranjan, Dikran N., 1950- ; Lukács, Gábor, 1982-
    In this paper, we show that for every locally compact abelian group ▫$G$▫, the following statements are equivalent: (i) ▫$G$▫ contains no sequence ▫$\{x_n\}_{n=0}^\infty$▫ such that ▫$\{0\} \cup ... \{\pm x_n \vert n \in {\mathbb N}$▫ is infinite and quasi-convex in ▫$G$▫, and ▫$x_n \to 0$▫; (ii) one of the subgroups ▫$\{g \in G \vert 2g=0\}$▫ or ▫$\{g \in G \vert 3g=0\}$▫ is open in ▫$G$▫; (iii) ▫$G$▫ contains an open compact subgroup of the form ▫${\mathbb Z}_2^\kappa$▫ or ▫${\mathbb Z}_3^\kappa$▫ for some cardinal ▫$\kappa$▫.
    Source: Journal of Pure and Applied Algebra. - ISSN 0022-4049 (Vol. 214, iss. 6, 2010, str. 885-897)
    Type of material - article, component part
    Publish date - 2010
    Language - english
    COBISS.SI-ID - 15630937

    Link(s):

    http://dx.doi.org/10.1016/j.jpaa.2009.08.006

source: Journal of Pure and Applied Algebra. - ISSN 0022-4049 (Vol. 214, iss. 6, 2010, str. 885-897)

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