{"paper":{"title":"Characterizations of Ideal Cluster Points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.GN","math.NT","math.PR"],"primary_cat":"math.CA","authors_text":"Fabio Maccheroni, Paolo Leonetti","submitted_at":"2017-07-11T14:07:33Z","abstract_excerpt":"Given an ideal $\\mathcal{I}$ on $\\omega$, we prove that a sequence in a topological space $X$ is $\\mathcal{I}$-convergent if and only if there exists a ``big'' $\\mathcal{I}$-convergent subsequence. Then, we study several properties and show two characterizations of the set of $\\mathcal{I}$-cluster points as classical cluster points of a filters on $X$ and as the smallest closed set containing ``almost all'' the sequence. As a consequence, we obtain that the underlying topology $\\tau$ coincides with the topology generated by the pair $(\\tau,\\mathcal{I})$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.03281","kind":"arxiv","version":4},"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"}