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Projectively universal countable metrizable groups


Authors: Vladimir G. Pestov and Vladimir V. Uspenskij
Journal: Proc. Amer. Math. Soc. 144 (2016), 4527-4532
MSC (2010): Primary 22A05
DOI: https://doi.org/10.1090/proc/13189
Published electronically: May 31, 2016
MathSciNet review: 3531199
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Abstract: We prove that there exists a countable metrizable topological group $ G$ such that every countable metrizable group is isomorphic to a quotient of $ G$. The completion $ H$ of $ G$ is a Polish group such that every Polish group is isomorphic to a quotient of $ H$.


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Additional Information

Vladimir G. Pestov
Affiliation: Department of Mathematics and Statistics, University of Ottawa, Ottawa, Ontario, Canada K1N 6N5 — and — Departamento de Matemática, Universidade Federal de Santa Catarina, Trindade, Florianópolis, Santa Catarina, 88.040-900, Brazil
Email: vpest283@uottawa.ca

Vladimir V. Uspenskij
Affiliation: Department of Mathematics, 321 Morton Hall, Ohio University, Athens, Ohio 45701
Email: uspenski@ohio.edu

DOI: https://doi.org/10.1090/proc/13189
Keywords: Polish group, couniversal, completion, quotient group
Received by editor(s): September 14, 2014
Received by editor(s) in revised form: October 27, 2015
Published electronically: May 31, 2016
Additional Notes: The first author was a Special Visiting Researcher of the program Science Without Borders of CAPES (Brazil), processo 085/2012
Communicated by: Mirna Džamonja
Article copyright: © Copyright 2016 American Mathematical Society