English

Projectively universal countable metrizable groups

Group Theory 2021-08-31 v2

Abstract

We prove that there exists a countable metrizable topological group GG such that every countable metrizable group is isomorphic to a quotient of GG. The completion HH of GG is a Polish group such that every Polish group is isomorphic to a quotient of HH.

Keywords

Cite

@article{arxiv.1409.4108,
  title  = {Projectively universal countable metrizable groups},
  author = {Vladimir G. Pestov and Vladimir V. Uspenskij},
  journal= {arXiv preprint arXiv:1409.4108},
  year   = {2021}
}

Comments

7 pages, latex 2e. The proof at the end of Section 3 has been expanded, minor inaccuracies fixed

R2 v1 2026-06-22T05:56:25.279Z