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Metrically universal abelian groups

  1. 1. 0474420 - MU-W 2018 RIV US eng J - Článek v odborném periodiku
    Doucha, Michal
    Metrically universal abelian groups.
    American Mathematical Society. Transactions. Roč. 369, č. 8 (2017), s. 5981-5998. ISSN 0002-9947
    Grant CEP: GA AV ČR IAA100190902
    Institucionální podpora: RVO:67985840
    Klíčová slova: Abelian group
    Kód oboru RIV: BA - Obecná matematika
    Obor OECD: Pure mathematics
    Impakt faktor: 1.496, rok: 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.
    Trvalý link: http://hdl.handle.net/11104/0271474
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