2015/10/01 by Itaï Ben Yaacov, Yaacov, Itaï Ben · 1 citation
Arts and Humanities · Mathematics · Social Sciences · #Advanced Operator Algebra Research #Advanced Topology and Set Theory #FOS: Mathematics #Language and Culture #Limits and Structures in Graph Theory #Logic (math.LO) #Polish-Jewish Holocaust Memory Studies
paper · pdf · doi:10.48550/arxiv.1510.00238
openalex publication_date 2015/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study when a continuous isometric action of a Polish group on a complete metric space is, or can be, transitive. Our main results consist of showing that certain Polish groups, namely Aut^*(μ) and Homeo+[0,1], such an action can never be transitive (unless the space acted upon is a singleton). We also point out "circumstantial evidence" that this pathology could be related to that of Polish groups which are not closed permutation groups and yet have discrete uniform distance, and give a general characterisation of continuous isometric action of a Roeckle-precompact Polish group on a complete metric space is transitive. It follows that the morphism from a Roeckle-precompact Polish group to its Bohr compactification is surjective.