{"paper":{"title":"On Roeckle-precompact Polish group which cannot act transitively on a complete metric space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Ita\\\"i Ben Yaacov (ICJ)","submitted_at":"2015-10-01T13:58:46Z","abstract_excerpt":"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 $\\mathrm{Aut}^*(\\mu)$ and $\\mathrm{Homeo}^+[0,1]$, 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-precompac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.00238","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}