{"paper":{"title":"On strongly separately continuous functions on sequence spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Olena Karlova, Tom\\'a\\v{s} Visnyai","submitted_at":"2015-12-06T07:51:26Z","abstract_excerpt":"We study strongly separately continuous real-valued function defined on the Banach spaces $\\ell_p$. Determining sets for the class of strongly separately continuous functions on $\\ell_p$ are characterized. We prove that for every $1\\le \\alpha<\\omega_1$ there exists a strongly separately continuous function which belongs the $(\\alpha+1)$'th Baire class and does not belong to the $\\alpha$'th Baire class on $\\ell_p$. We show that any open set in $\\ell_p$ is the set of discontinuities of a strongly separately continuous real-valued function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.01757","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"}