Vladimir Pestov, Vladimir Uspenskij
Abstract
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We prove that there exists a countable metrizable topological group G G such that every countable metrizable group is isomorphic to a quotient of G G . The completion H H of G G is a Polish group such that every Polish group is isomorphic to a quotient of H H .
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We prove that there exists a countable metrizable topological group G G such that every countable metrizable group is isomorphic to a quotient of G G . The completion H H of G G is a Polish group such that every Polish group is isomorphic to a quotient of H H .
Key concepts: Metrization theorem, Countable set, Mathematics, Quotient, Group (periodic table), Topological group, Quotient group, Pure mathematics