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  • Each topological group embeds into a duoseparable topological group
    Banakh, Taras, 1968- ; Guran, Igor ; Ravsky, O. V.
    A topological group ▫$X$▫ is called "duoseparable" if there exists a countable set ▫$S\subseteq X$▫ such that ▫$SUS=X$▫ for any neighborhood ▫$U\subseteq X$▫ of the identity. We construct a functor ... ▫$F$▫ assigning to each (abelian) topological group ▫$X$▫ a duoseparable (abelain-by-cyclic) topological group ▫$FX$▫, containing an isomorphic copy of ▫$X$▫. In fact, the functor ▫$F$▫ is defined on the category of unital topologized magmas. Also we prove that each ▫$\sigma$▫-compact locally compact abelian topological group embeds into a duoseparable locally compact abelian-by-countable locally compact topological group.
    Source: Topology and its Applications. - ISSN 0166-8641 (Vol. 289, Feb. 2021, art. 107487 (10 str.))
    Type of material - article, component part ; adult, serious
    Publish date - 2021
    Language - english
    COBISS.SI-ID - 45529347

    Link(s):

    https://doi.org/10.1016/j.topol.2020.107487
    DOI

source: Topology and its Applications. - ISSN 0166-8641 (Vol. 289, Feb. 2021, art. 107487 (10 str.))
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