{"paper":{"title":"The cross-topology and Lebesgue triples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Olena Karlova, Volodymyr Mykhaylyuk","submitted_at":"2016-01-22T07:53:09Z","abstract_excerpt":"The cross topology $\\gamma$ on a product of topological spaces $X$ and $Y$ is the collection of all sets $G\\subseteq X\\times Y$ such that the intersection of $G$ with every vertical line and every horizontal line is an open subset of either vertical or horizontal line, respectively.\n  For spaces $X$ and $Y$ from a wide class, which includes all spaces $\\mathbb R^n$, we prove that there exists a separately continuous mapping $f:X\\times Y\\to (X\\times Y,\\gamma)$ which is not a pointwise limit of a sequence of continuous functions. Also we prove that every separately continuous mapping is a pointw"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05897","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"}