Every Polish group has a non-trivial topological group automorphism

2024/08/28 by Estrada, Carlos Pérez, Ramos-García, Ulises Ariet
#03E15 #54H11 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2408.16162

Abstract

We prove that every Polish group with more than two elements admits a non-trivial topological group automorphism. As a consequence, a hypothetical uniquely homogeneous Polish space with more than two points cannot be a semitopological group.

Related

• Some Results on Polish Groups
• Polish topologies on groups of non-singular transformations
• \mathop\rm PL₊(I) is not a Polish group
• Isometry groups of Polish ultrametric spaces
• Chief factors in Polish groups