{"paper":{"title":"Komlos Properties in Banach Lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"E. Y. Emelyanov, N. Erkursun Ozcan, S. G. Gorokhova","submitted_at":"2017-10-06T20:41:25Z","abstract_excerpt":"Several Koml\\'os like properties in Banach lattices are investigated. We prove that $C(K)$ fails the $oo$-pre-Koml\\'os property, assuming that the compact Hausdorff space $K$ has a nonempty separable open subset $U$ without isolated points such that every $u\\in U$ has countable neighborhood base. We prove also that for any infinite dimensional Banach lattice $E$ there is an unbounded convex $uo$-pre-Koml\\'os set $C\\subseteq E_+$ which is not $uo$-Koml\\'os."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.02580","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"}