Metrically universal abelian groups

0474420 - MÚ 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. E-ISSN 1088-6850
Grant CEP: GA AV ČR IAA100190902
Institucionální podpora: RVO:67985840
Klíčová slova: Abelian group
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