{"paper":{"title":"Additivity and lineability in vector spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Artur Bartoszewicz, Szymon G\\l\\cab","submitted_at":"2013-04-25T09:47:01Z","abstract_excerpt":"G\\'amez-Merino, Munoz-Fern\\'andez and Seoane-Sep\\'ulveda proved that if additivity $\\mathcal A(\\mathcal F)>\\mathfrak c$, then $\\mathcal F$ is $\\mathcal A(\\mathcal F)$-lineable where $\\mathcal F\\subseteq\\mathbb R^\\mathbb R$. They asked if $\\mathcal A(\\mathcal F)>\\mathfrak c$ can be weakened. We answer this question in negative. Moreover, we introduce and study the notions of homogeneous lineability number and lineability number of subsets of linear spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.6848","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"}