{"paper":{"title":"A study concerning splitting and jointly continuous topologies on $C(Y,Z)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Athanasios Megaritis, Dimitris Georgiou, Kyriakos Papadopoulos, Vasilios Petropoulos","submitted_at":"2018-01-01T09:39:27Z","abstract_excerpt":"Let $Y$ and $Z$ be two fixed topological spaces and $C(Y,Z)$ the set of all continuous maps from $Y$ into $Z$. We construct and study topologies on $C(Y,Z)$ that we call ${\\cal F}_n(\\tau_n)$-family-open topologies. Furthermore, we find necessary and sufficient conditions such that these topologies to be splitting and jointly continuous. Finally, we present questions concerning a further study on this area."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.00419","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"}