Every Polish group has a non-trivial topological group automorphism

Autor:	Estrada, Carlos Pérez, Ramos-García, Ulises Ariet
Rok vydání:	2024
Předmět:	Mathematics - Logic 03E15 54H11
Druh dokumentu:	Working Paper
Popis:	We prove that every Polish group admits a non-trivial topological group automorphism. This answers a question posed by Forte Shinko. As a consequence, we prove that there are no uniquely homogeneous Polish groups. Comment: The argument in the last paragraph of the proof of Theorem 1.1 is faulty. Concretely, when we extend a non-trivial automorphism of L to the whole group by fixing any element of a maximal independent subset Y of U, we redefine the automorphism for the elements of L that are generated by Y. We thank Forte Shinko for pointing out this mistake
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2408.16162 Zobrazit plný text záznamu View this record from Arxiv