{"paper":{"title":"Lineability, spaceability, and additivity cardinals for Darboux-like functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Daniel Pellegrino, Jos\\'e L. G\\'amez-Merino, Juan B. Seoane-Sep\\'ulveda, Krzysztof Chris Ciesielski","submitted_at":"2013-09-08T15:12:26Z","abstract_excerpt":"We introduce the concept of {\\em maximal lineability cardinal number}, $\\mL(M)$, of a subset $M$ of a topological vector space and study its relation to the cardinal numbers known as: additivity $A(M)$, homogeneous lineability $\\HL(M)$, and lineability $\\LL(M)$ of $M$. In particular, we will describe, in terms of $\\LL$, the lineability and spaceability of the families of the following Darboux-like functions on $\\real^n$, $n\\ge 1$: extendable, Jones, and almost continuous functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1965","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"}