{"paper":{"title":"Topological complexity of ideal limit points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.FA"],"primary_cat":"math.GN","authors_text":"Marek Balcerzak, Paolo Leonetti, Szymon Glab","submitted_at":"2024-07-16T20:32:42Z","abstract_excerpt":"Given an ideal $\\mathcal{I}$ on the nonnegative integers $\\omega$ and a Polish space $X$, let $\\mathscr{L}(\\mathcal{I})$ be the family of subsets $S\\subseteq X$ such that $S$ is the set of $\\mathcal{I}$-limit points of some sequence taking values in $X$. First, we show that $\\mathscr{L}(\\mathcal{I})$ may attain arbitrarily large Borel complexity. Second, we prove that if $\\mathcal{I}$ is a $G_{\\delta\\sigma}$-ideal then all elements of $\\mathscr{L}(\\mathcal{I})$ are closed. Third, we show that if $\\mathcal{I}$ is a simply coanalytic ideal and $X$ is first countable, then every element of $\\math"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.12160","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2407.12160/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}