{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:7NENYQ6JM7IB3DD4TBWLKMMI57","short_pith_number":"pith:7NENYQ6J","schema_version":"1.0","canonical_sha256":"fb48dc43c967d01d8c7c986cb53188efeb8572e44fe0c1da3df4abca5f5ef887","source":{"kind":"arxiv","id":"1408.4930","version":1},"attestation_state":"computed","paper":{"title":"Nonlinear order isomorphisms on function spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Denny H. Leung, Wee-Kee Tang","submitted_at":"2014-08-21T09:29:26Z","abstract_excerpt":"Let $X$ be a topological space. A subset of $C(X)$, the space of continuous real-valued functions on $X$, is a partially ordered set in the pointwise order. Suppose that $X$ and $Y$ are topological spaces, and $A(X)$ and $A(Y)$ are subsets of $C(X)$ and $C(Y)$ respectively. We consider the general problem of characterizing the order isomorphisms (order preserving bijections) between $A(X)$ and $A(Y)$. Under some general assumptions on $A(X)$ and $A(Y)$, and when $X$ and $Y$ are compact Hausdorff, it is shown that existence of an order isomorphism between $A(X)$ and $A(Y)$ gives rise to an asso"},"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":"1408.4930","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-08-21T09:29:26Z","cross_cats_sorted":[],"title_canon_sha256":"25c9dfc93e448acbb8b03233c48f4daa6f1509c5412f2592e2c884595c7f2d47","abstract_canon_sha256":"5c58b4ede3abf548ab6158c48a6d097c0971adf39a45dc36e70e2aad5c860edb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:41.252847Z","signature_b64":"95XvohaX5eGq8hRIwY7dNe7CfE+8Ot0xdLDxkUonYmxamBuhTGoAk/wUdUgHGZbHRvfE9m/j+91Qpvee58pSDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fb48dc43c967d01d8c7c986cb53188efeb8572e44fe0c1da3df4abca5f5ef887","last_reissued_at":"2026-05-18T02:44:41.252436Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:41.252436Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nonlinear order isomorphisms on function spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Denny H. Leung, Wee-Kee Tang","submitted_at":"2014-08-21T09:29:26Z","abstract_excerpt":"Let $X$ be a topological space. A subset of $C(X)$, the space of continuous real-valued functions on $X$, is a partially ordered set in the pointwise order. Suppose that $X$ and $Y$ are topological spaces, and $A(X)$ and $A(Y)$ are subsets of $C(X)$ and $C(Y)$ respectively. We consider the general problem of characterizing the order isomorphisms (order preserving bijections) between $A(X)$ and $A(Y)$. Under some general assumptions on $A(X)$ and $A(Y)$, and when $X$ and $Y$ are compact Hausdorff, it is shown that existence of an order isomorphism between $A(X)$ and $A(Y)$ gives rise to an asso"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.4930","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":"1408.4930","created_at":"2026-05-18T02:44:41.252489+00:00"},{"alias_kind":"arxiv_version","alias_value":"1408.4930v1","created_at":"2026-05-18T02:44:41.252489+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.4930","created_at":"2026-05-18T02:44:41.252489+00:00"},{"alias_kind":"pith_short_12","alias_value":"7NENYQ6JM7IB","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_16","alias_value":"7NENYQ6JM7IB3DD4","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_8","alias_value":"7NENYQ6J","created_at":"2026-05-18T12:28:19.803747+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/7NENYQ6JM7IB3DD4TBWLKMMI57","json":"https://pith.science/pith/7NENYQ6JM7IB3DD4TBWLKMMI57.json","graph_json":"https://pith.science/api/pith-number/7NENYQ6JM7IB3DD4TBWLKMMI57/graph.json","events_json":"https://pith.science/api/pith-number/7NENYQ6JM7IB3DD4TBWLKMMI57/events.json","paper":"https://pith.science/paper/7NENYQ6J"},"agent_actions":{"view_html":"https://pith.science/pith/7NENYQ6JM7IB3DD4TBWLKMMI57","download_json":"https://pith.science/pith/7NENYQ6JM7IB3DD4TBWLKMMI57.json","view_paper":"https://pith.science/paper/7NENYQ6J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1408.4930&json=true","fetch_graph":"https://pith.science/api/pith-number/7NENYQ6JM7IB3DD4TBWLKMMI57/graph.json","fetch_events":"https://pith.science/api/pith-number/7NENYQ6JM7IB3DD4TBWLKMMI57/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7NENYQ6JM7IB3DD4TBWLKMMI57/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7NENYQ6JM7IB3DD4TBWLKMMI57/action/storage_attestation","attest_author":"https://pith.science/pith/7NENYQ6JM7IB3DD4TBWLKMMI57/action/author_attestation","sign_citation":"https://pith.science/pith/7NENYQ6JM7IB3DD4TBWLKMMI57/action/citation_signature","submit_replication":"https://pith.science/pith/7NENYQ6JM7IB3DD4TBWLKMMI57/action/replication_record"}},"created_at":"2026-05-18T02:44:41.252489+00:00","updated_at":"2026-05-18T02:44:41.252489+00:00"}