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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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1710.06878","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2017-10-18T18:06:40Z","cross_cats_sorted":[],"title_canon_sha256":"cfdf2eca3d5d2b8b7a2a21d0d8832c8987af585eba06cf991a4e413bfc862679","abstract_canon_sha256":"b00068226743e13ddd294878b015c8398c7543bd76a3d6ba38fe453a2c6dd536"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:30.046218Z","signature_b64":"gy2z8r4zwk9nTrOhEq7r5ymmkkyjRO1Q4089gPyLgvMALAJCJnd+WUuLtZ9J+fwFHLSEZYwFXY2qDL/IDGKPDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ae6c07058f74a51595e976e1fb960719398c06d75ccd9e9241ddf268300106c","last_reissued_at":"2026-05-18T00:32:30.045448Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:30.045448Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1710.06878","created_at":"2026-05-18T00:32:30.045568+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.06878v1","created_at":"2026-05-18T00:32:30.045568+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.06878","created_at":"2026-05-18T00:32:30.045568+00:00"},{"alias_kind":"pith_short_12","alias_value":"DLTMA4CY65FF","created_at":"2026-05-18T12:31:10.602751+00:00"},{"alias_kind":"pith_short_16","alias_value":"DLTMA4CY65FFCWK6","created_at":"2026-05-18T12:31:10.602751+00:00"},{"alias_kind":"pith_short_8","alias_value":"DLTMA4CY","created_at":"2026-05-18T12:31:10.602751+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DLTMA4CY65FFCWK6S5XB7OLAOG","json":"https://pith.science/pith/DLTMA4CY65FFCWK6S5XB7OLAOG.json","graph_json":"https://pith.science/api/pith-number/DLTMA4CY65FFCWK6S5XB7OLAOG/graph.json","events_json":"https://pith.science/api/pith-number/DLTMA4CY65FFCWK6S5XB7OLAOG/events.json","paper":"https://pith.science/paper/DLTMA4CY"},"agent_actions":{"view_html":"https://pith.science/pith/DLTMA4CY65FFCWK6S5XB7OLAOG","download_json":"https://pith.science/pith/DLTMA4CY65FFCWK6S5XB7OLAOG.json","view_paper":"https://pith.science/paper/DLTMA4CY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.06878&json=true","fetch_graph":"https://pith.science/api/pith-number/DLTMA4CY65FFCWK6S5XB7OLAOG/graph.json","fetch_events":"https://pith.science/api/pith-number/DLTMA4CY65FFCWK6S5XB7OLAOG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DLTMA4CY65FFCWK6S5XB7OLAOG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DLTMA4CY65FFCWK6S5XB7OLAOG/action/storage_attestation","attest_author":"https://pith.science/pith/DLTMA4CY65FFCWK6S5XB7OLAOG/action/author_attestation","sign_citation":"https://pith.science/pith/DLTMA4CY65FFCWK6S5XB7OLAOG/action/citation_signature","submit_replication":"https://pith.science/pith/DLTMA4CY65FFCWK6S5XB7OLAOG/action/replication_record"}},"created_at":"2026-05-18T00:32:30.045568+00:00","updated_at":"2026-05-18T00:32:30.045568+00:00"}