{"paper":{"title":"Admissible topologies on $C(Y,Z)$ and ${\\cal O}_Z(Y)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Athanasios Megaritis, Dimitris Georgiou, Kyriakos Papadopoulos","submitted_at":"2017-10-18T18:06:40Z","abstract_excerpt":"Let $Y$ and $Z$ be two given topological spaces, ${\\cal O}(Y)$ (respectively, ${\\cal O}(Z)$) the set of all open subsets of $Y$ (respectively, $Z$), and $C(Y,Z)$ the set of all continuous maps from $Y$ to $Z$. We study Scott type topologies on ${\\mathcal O}(Y)$ and we construct admissible topologies on $C(Y,Z)$ and ${\\mathcal O}_Z(Y)=\\{f^{-1}(U)\\in {\\mathcal O}(Y): f\\in C(Y,Z)\\ {\\rm and}\\ U\\in {\\mathcal O}(Z)\\}$, introducing new problems in the field."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.06878","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"}