{"paper":{"title":"Characterizations of the Ideal Core","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.FA","authors_text":"Paolo Leonetti","submitted_at":"2019-05-01T21:55:59Z","abstract_excerpt":"Given an ideal $\\mathcal{I}$ on $\\omega$ and a sequence $x$ in a topological vector space, we let the $\\mathcal{I}$-core of $x$ be the least closed convex set containing $\\{x_n: n \\notin I\\}$ for all $I \\in \\mathcal{I}$. We show two characterizations of the $\\mathcal{I}$-core. This implies that the $\\mathcal{I}$-core of a bounded sequence in $\\mathbf{R}^k$ is simply the convex hull of its $\\mathcal{I}$-cluster points. As applications, we simplify and extend several results in the context of Pringsheim-convergence and $e$-convergence of double sequences."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.00514","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"}