{"paper":{"title":"Topological and measure properties of some self-similar sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Artur Bartoszewicz, Emilia Szymonik, Malgorzata Filipczak, Taras Banakh","submitted_at":"2014-03-01T15:43:44Z","abstract_excerpt":"Given a finite subset $\\Sigma\\subset\\mathbb{R}$ and a positive real number $q<1$ we study topological and measure-theoretic properties of the self-similar set $K(\\Sigma;q)=\\big\\{\\sum_{n=0}^\\infty a_nq^n:(a_n)_{n\\in\\omega}\\in\\Sigma^\\omega\\big\\}$, which is the unique compact solution of the equation $K=\\Sigma+qK$. The obtained results are applied to studying partial sumsets $E(x)=\\big\\{\\sum_{n=0}^\\infty x_n\\varepsilon_n:(\\varepsilon_n)_{n\\in\\omega}\\in\\{0,1\\}^\\omega\\big\\}$ of some (multigeometric) sequences $x=(x_n)_{n\\in\\omega}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.0098","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"}