{"paper":{"title":"On meager function spaces, network character and meager convergence in topological spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Lyubomyr Zdomskyy, Taras Banakh, Volodymyr Mykhaylyuk","submitted_at":"2010-12-12T08:21:44Z","abstract_excerpt":"For a non-isolated point $x$ of a topological space $X$ the network character $nw_\\chi(x)$ is the smallest cardinality of a family of infinite subsets of $X$ such that each neighborhood $O(x)$ of $x$ contains a set from the family. We prove that (1) each infinite compact Hausdorff space $X$ contains a non-isolated point $x$ with $nw_\\chi(x)=\\aleph_0$; (2) for each point $x\\in X$ with countable character there is an injective sequence in $X$ that $\\F$-converges to $x$ for some meager filter $\\F$ on $\\omega$; (3) if a functionally Hausdorff space $X$ contains an $\\F$-convergent injective sequenc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.2522","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"}