2021/10/14 by François Le Maître, Maître, François Le
Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #Group Theory (math.GR) #Logic (math.LO) #math.GR #math.LO
paper · pdf · doi:10.48550/arxiv.2110.07289
Reworked notation to make it more coherent. Comments welcome!
openalex publication_date 2021/10/14 · arxiv created 2022/01/21 · arxiv updated 2022/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we prove several results concerning Polish group topologies on groups of non-singular transformation. We first prove that the group of measure-preserving transformations of the real line whose support has finite measure carries no Polish group topology. We then characterize the Borel σ-finite measures λ on a standard Borel space for which the group of λ-preserving transformations has the automatic continuity property. We finally show that the natural Polish topology on the group of all non-singular transformations is actually its only Polish group topology.