{"paper":{"title":"Dynamical quasitilings of amenable group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Dawid Huczek, Tomasz Downarowicz","submitted_at":"2017-05-20T22:33:55Z","abstract_excerpt":"We prove that for any compact zero-dimensional metric space $X$ on which an infinite countable amenable group $G$ acts freely by homeomorphisms, there exists a dynamical quasitiling with good covering, continuity, F{\\o}lner and dynamical properties, i.e to every $x\\in X$ we can assign a quasitiling $\\mathcal{T}_x$ of $G$ (with all the $\\mathcal{T}_x$ using the same, finite set of shapes) such that the tiles of $\\mathcal{T}_x$ are disjoint, their union has arbitrarily high lower Banach Density, all the shapes of $\\mathcal{T}_x$ are large subsets of an arbitrarily large F{\\o}lner set, and if we "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.07365","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"}