{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:MALXRYYBVFUSTJI2XPE7ZGZ524","short_pith_number":"pith:MALXRYYB","schema_version":"1.0","canonical_sha256":"601778e301a96929a51abbc9fc9b3dd70a34288491fc2fa9e002b85fd60d177a","source":{"kind":"arxiv","id":"1812.10166","version":2},"attestation_state":"computed","paper":{"title":"The $\\kappa$-Fr\\'{e}chet--Urysohn property for locally convex spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.GN","authors_text":"S. Gabriyelyan","submitted_at":"2018-12-25T21:11:39Z","abstract_excerpt":"A topological space $X$ is $\\kappa$-Fr\\'{e}chet--Urysohn if for every open subset $U$ of $X$ and every $x\\in \\overline{U}$ there exists a sequence in $ U$ converging to $x$. We prove that every $\\kappa$-Fr\\'{e}chet--Urysohn Tychonoff space $X$ is Ascoli. We apply this statement and some of known results to characterize the $\\kappa$-Fr\\'echet--Urysohn property in various important classes of locally convex spaces. In particular, answering a question posed in [7] we obtain that $C_p(X)$ is Ascoli iff $X$ has the property $(\\kappa)$."},"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":"1812.10166","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2018-12-25T21:11:39Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"059bc7431c7b0fe6da6b52a562c93606c7bf0ff3d03b50b90694daec0c904dc1","abstract_canon_sha256":"259af0e011f033b9febfc6c7da6034e60df9cdf077ba71ab6d2e2834b6e34082"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:52.465997Z","signature_b64":"8YtP7AtV+xli8ena+vdaZn50HeC/ybjhnfjupdsvnqFQViQGioLJGaUILV9NR6yAtMIGqDlR7nKMhw0CxDSUCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"601778e301a96929a51abbc9fc9b3dd70a34288491fc2fa9e002b85fd60d177a","last_reissued_at":"2026-05-17T23:56:52.465548Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:52.465548Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The $\\kappa$-Fr\\'{e}chet--Urysohn property for locally convex spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.GN","authors_text":"S. Gabriyelyan","submitted_at":"2018-12-25T21:11:39Z","abstract_excerpt":"A topological space $X$ is $\\kappa$-Fr\\'{e}chet--Urysohn if for every open subset $U$ of $X$ and every $x\\in \\overline{U}$ there exists a sequence in $ U$ converging to $x$. We prove that every $\\kappa$-Fr\\'{e}chet--Urysohn Tychonoff space $X$ is Ascoli. We apply this statement and some of known results to characterize the $\\kappa$-Fr\\'echet--Urysohn property in various important classes of locally convex spaces. In particular, answering a question posed in [7] we obtain that $C_p(X)$ is Ascoli iff $X$ has the property $(\\kappa)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.10166","kind":"arxiv","version":2},"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":"1812.10166","created_at":"2026-05-17T23:56:52.465612+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.10166v2","created_at":"2026-05-17T23:56:52.465612+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.10166","created_at":"2026-05-17T23:56:52.465612+00:00"},{"alias_kind":"pith_short_12","alias_value":"MALXRYYBVFUS","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_16","alias_value":"MALXRYYBVFUSTJI2","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_8","alias_value":"MALXRYYB","created_at":"2026-05-18T12:32:37.024351+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/MALXRYYBVFUSTJI2XPE7ZGZ524","json":"https://pith.science/pith/MALXRYYBVFUSTJI2XPE7ZGZ524.json","graph_json":"https://pith.science/api/pith-number/MALXRYYBVFUSTJI2XPE7ZGZ524/graph.json","events_json":"https://pith.science/api/pith-number/MALXRYYBVFUSTJI2XPE7ZGZ524/events.json","paper":"https://pith.science/paper/MALXRYYB"},"agent_actions":{"view_html":"https://pith.science/pith/MALXRYYBVFUSTJI2XPE7ZGZ524","download_json":"https://pith.science/pith/MALXRYYBVFUSTJI2XPE7ZGZ524.json","view_paper":"https://pith.science/paper/MALXRYYB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.10166&json=true","fetch_graph":"https://pith.science/api/pith-number/MALXRYYBVFUSTJI2XPE7ZGZ524/graph.json","fetch_events":"https://pith.science/api/pith-number/MALXRYYBVFUSTJI2XPE7ZGZ524/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MALXRYYBVFUSTJI2XPE7ZGZ524/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MALXRYYBVFUSTJI2XPE7ZGZ524/action/storage_attestation","attest_author":"https://pith.science/pith/MALXRYYBVFUSTJI2XPE7ZGZ524/action/author_attestation","sign_citation":"https://pith.science/pith/MALXRYYBVFUSTJI2XPE7ZGZ524/action/citation_signature","submit_replication":"https://pith.science/pith/MALXRYYBVFUSTJI2XPE7ZGZ524/action/replication_record"}},"created_at":"2026-05-17T23:56:52.465612+00:00","updated_at":"2026-05-17T23:56:52.465612+00:00"}