{"paper":{"title":"Limit points of subsequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.PR"],"primary_cat":"math.GN","authors_text":"Paolo Leonetti","submitted_at":"2017-12-31T19:38:41Z","abstract_excerpt":"Let $x$ be a sequence taking values in a separable metric space and $\\mathcal{I}$ be a generalized density ideal or an $F_\\sigma$-ideal on the positive integers (in particular, $\\mathcal{I}$ can be any Erd{\\H o}s--Ulam ideal or any summable ideal). It is shown that the collection of subsequences of $x$ which preserve the set of $\\mathcal{I}$-cluster points of $x$ [respectively, $\\mathcal{I}$-limit points] is of second category if and only if the set of $\\mathcal{I}$-cluster points of $x$ [resp., $\\mathcal{I}$-limit points] coincides with the set of ordinary limit points of $x$; moreover, in th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.00343","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"}