{"paper":{"title":"Smooth automorphisms and path-connectedness in Borel dynamics","license":"","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Konstantin Medynets, Sergey Bezuglyi","submitted_at":"2004-10-23T09:23:03Z","abstract_excerpt":"Let $Aut(X,\\mathcal{B})$ be the group of all Borel automorphisms of a standard Borel space $(X,\\mathcal{B})$. We study topological properties of $Aut(X,\\mathcal{B})$ with respect to the uniform and weak topologies, $\\tau$ and $p$, defined in [Bezuglyi S., Dooley A.H., Kwiatkowski J., Topologies on the group of Borel automorphisms of a standard Borel space, Preprint, 2003]. It is proved that the class of smooth automorphisms is dense in $(Aut(X,\\mathcal B),p)$. Let $Ctbl(X)$ denote the group of Borel automorphisms with countable support. It is shown that the topological group $Aut_0(X,\\mathcal "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0410504","kind":"arxiv","version":1},"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"}