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Metrically universal abelian groups

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    0474420 - MÚ 2018 RIV US eng J - Journal Article
    Doucha, Michal
    Metrically universal abelian groups.
    American Mathematical Society. Transactions. Roč. 369, č. 8 (2017), s. 5981-5998. ISSN 0002-9947. E-ISSN 1088-6850
    R&D Projects: GA AV ČR IAA100190902
    Institutional support: RVO:67985840
    Keywords : Abelian group
    OECD category: Pure mathematics
    Impact factor: 1.496, year: 2017
    http://www.ams.org/journals/tran/2017-369-08/S0002-9947-2017-07059-8/

    We give a positive answer to the question of Shkarin (Mat. Sb. 190 (1999), no. 7, 127-144) whether there exists a metrically universal abelian separable group equipped with invariant metric. Our construction also gives an example of a group structure on the Urysohn universal space that is substantially different from the previously known examples. Under some cardinal arithmetic assumptions, our results generalize to higher cardinalities.
    Permanent Link: http://hdl.handle.net/11104/0271474

     
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