{"paper":{"title":"On approximation of homeomorphisms of a Cantor set","license":"","headline":"","cross_cats":["math.GR"],"primary_cat":"math.DS","authors_text":"Konstantin Medynets","submitted_at":"2005-10-03T07:34:45Z","abstract_excerpt":"We continue to study topological properties of the group Homeo(X) of all homeomorphisms of a Cantor set X with respect to the uniform topology tau, which was started in the paper (S. Bezuglyi, A.H. Dooley, and J. Kwiatkowski, Topologies on the group of homeomorphisms of a Cantor set, ArXiv e-print math.DS/0410507, 2004). We prove that the set of periodic homeomorphisms is tau-dense in Homeo(X) and deduce from this result that the topological group (Homeo(X), tau) has the Rokhlin property, i.e., there exists a homeomorphism whose conjugate class is tau-dense in Homeo(X). We also show that for a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0510032","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"}