2011/09/11 by Longyun Ding, Ding, Longyun
Mathematics · #03E15 54H11 54H05 #Advanced Topology and Set Theory #FOS: Mathematics #Geometric and Algebraic Topology #Logic (math.LO) #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.1109.2283
openalex publication_date 2011/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A Polish group is surjectively universal if it can be continuously homomorphically mapped onto every Polish group. Making use of a type of new metrics on free groups \citeDG, we prove the existence of surjectively universal Polish groups, answering in the positive a question of Kechris. In fact, we give several examples of surjectively universal Polish groups. We find a sufficient condition to guarantee that the new metrics on free groups can be computed directly. We also compare this condition with CLI groups.