{"paper":{"title":"On Baire classification of strongly separately continuous functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Olena Karlova","submitted_at":"2015-08-06T11:39:21Z","abstract_excerpt":"We investigate strongly separately continuous functions on a product of topological spaces and prove that if $X$ is a countable product of real lines, then there exists a strongly separately continuous function $f:X\\to\\mathbb R$ which is not Baire measurable. We show that if $X$ is a product of normed spaces $X_n$, $a\\in X$ and $\\sigma(a)=\\{x\\in X:|\\{n\\in\\mathbb N: x_n\\ne a_n\\}|<\\aleph_0\\}$ is a subspace of $X$, equipped with the Tychonoff topology, then for any open set $G\\subseteq \\sigma(a)$ there is a strongly separately continuous function $f:\\sigma(a)\\to \\mathbb R$ such that the discontin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01366","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"}