{"paper":{"title":"Algebraic and topological properties of some sets in $l_1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.GN","authors_text":"A. Bartoszewicz, E. Szymonik, Sz. Glab, T. Banakh","submitted_at":"2012-08-15T08:30:49Z","abstract_excerpt":"For a sequence $x \\in l_1 \\setminus c_{00}$, one can consider the set $E(x)$ of all subsums of series $\\sum_{n=1}^{\\infty} x(n)$. Guthrie and Nymann proved that $E(x)$ is one of the following types of sets:\n  (I) a finite union of closed intervals;\n  (C) homeomorphic to the Cantor set;\n  (MC) homeomorphic to the set $T$ of subsums of $\\sum_{n=1}^\\infty b(n)$ where $b(2n-1) = 3/4^n$ and $b(2n) = 2/4^n$.\n  By $I$, $C$ and $MC$ we denote the sets of all sequences $x \\in l_1 \\setminus c_{00}$, such that $E(x)$ has the corresponding property. In this note we show that $I$ and $C$ are strongly $\\mat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3058","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"}