Projectively universal countable metrizable groups

Pestov, Vladimir; Uspenskij, Vladimir

doi:10.1090/proc/13189

Projectively universal countable metrizable groups
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by Vladimir G. Pestov and Vladimir V. Uspenskij PDF

Proc. Amer. Math. Soc. 144 (2016), 4527-4532 Request permission

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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