{"paper":{"title":"On the set of limit points of conditionally convergent series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jacek Marchwicki, Szymon G{\\l}ab","submitted_at":"2016-04-21T11:05:53Z","abstract_excerpt":"Let $\\sum_{n=1}^\\infty x_n$ be a conditionally convergent series in a Banach space and let $\\tau$ be a permutation of natural numbers. We study the set $\\operatorname{LIM}(\\sum_{n=1}^\\infty x_{\\tau(n)})$ of all limit points of a sequence $(\\sum_{n=1}^p x_{\\tau(n)})_{p=1}^\\infty$ of partial sums of a rearranged series $\\sum_{n=1}^\\infty x_{\\tau(n)}$. We give full characterization of limit sets in finite dimensional spaces. Namely, a limit set in $\\mathbb{R}^m$ is either compact and connected or it is closed and all its connected components are unbounded. On the other hand each set of one of the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06255","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"}