{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1993:2BJFBU5CHZ44DBHSGFA52PX3JL","short_pith_number":"pith:2BJFBU5C","schema_version":"1.0","canonical_sha256":"d05250d3a23e79c184f23141dd3efb4af7843f169f8352cd8ec9ada5f74a7993","source":{"kind":"arxiv","id":"math/9303202","version":1},"attestation_state":"computed","paper":{"title":"Topologies on the set of all subspaces of a banach space and related questions of banach space geometry","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Mikhail I. Ostrovskii","submitted_at":"1993-03-29T17:51:57Z","abstract_excerpt":"For a Banach space $X$ we shall denote the set of all closed subspaces of $X$ by $G(X)$. In some kinds of problems it turned out to be useful to endow $G(X)$ with a topology. The main purpose of the present paper is to survey results on two the most common topologies on $G(X)$."},"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":"math/9303202","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.FA","submitted_at":"1993-03-29T17:51:57Z","cross_cats_sorted":[],"title_canon_sha256":"38ee3acae7394e5bcb545a0557f6ad616b40f0751ba588e810a943e9fc4dbe0d","abstract_canon_sha256":"09fe1b00a41698f548ce1e57e31365802f28fb90c6af2df977dac559edd064b2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:16.675168Z","signature_b64":"zZm6QOGmiwBGDRTEbmyPwIVZv6WuQHmMsn8uo0XMzKrpHdJPK8r1MrQHsnM41fxCjRbEX67z7XtQJy7KTjB6Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d05250d3a23e79c184f23141dd3efb4af7843f169f8352cd8ec9ada5f74a7993","last_reissued_at":"2026-05-18T04:41:16.674599Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:16.674599Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Topologies on the set of all subspaces of a banach space and related questions of banach space geometry","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Mikhail I. Ostrovskii","submitted_at":"1993-03-29T17:51:57Z","abstract_excerpt":"For a Banach space $X$ we shall denote the set of all closed subspaces of $X$ by $G(X)$. In some kinds of problems it turned out to be useful to endow $G(X)$ with a topology. The main purpose of the present paper is to survey results on two the most common topologies on $G(X)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9303202","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":"math/9303202","created_at":"2026-05-18T04:41:16.674678+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/9303202v1","created_at":"2026-05-18T04:41:16.674678+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9303202","created_at":"2026-05-18T04:41:16.674678+00:00"},{"alias_kind":"pith_short_12","alias_value":"2BJFBU5CHZ44","created_at":"2026-05-18T12:25:47.102015+00:00"},{"alias_kind":"pith_short_16","alias_value":"2BJFBU5CHZ44DBHS","created_at":"2026-05-18T12:25:47.102015+00:00"},{"alias_kind":"pith_short_8","alias_value":"2BJFBU5C","created_at":"2026-05-18T12:25:47.102015+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/2BJFBU5CHZ44DBHSGFA52PX3JL","json":"https://pith.science/pith/2BJFBU5CHZ44DBHSGFA52PX3JL.json","graph_json":"https://pith.science/api/pith-number/2BJFBU5CHZ44DBHSGFA52PX3JL/graph.json","events_json":"https://pith.science/api/pith-number/2BJFBU5CHZ44DBHSGFA52PX3JL/events.json","paper":"https://pith.science/paper/2BJFBU5C"},"agent_actions":{"view_html":"https://pith.science/pith/2BJFBU5CHZ44DBHSGFA52PX3JL","download_json":"https://pith.science/pith/2BJFBU5CHZ44DBHSGFA52PX3JL.json","view_paper":"https://pith.science/paper/2BJFBU5C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/9303202&json=true","fetch_graph":"https://pith.science/api/pith-number/2BJFBU5CHZ44DBHSGFA52PX3JL/graph.json","fetch_events":"https://pith.science/api/pith-number/2BJFBU5CHZ44DBHSGFA52PX3JL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2BJFBU5CHZ44DBHSGFA52PX3JL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2BJFBU5CHZ44DBHSGFA52PX3JL/action/storage_attestation","attest_author":"https://pith.science/pith/2BJFBU5CHZ44DBHSGFA52PX3JL/action/author_attestation","sign_citation":"https://pith.science/pith/2BJFBU5CHZ44DBHSGFA52PX3JL/action/citation_signature","submit_replication":"https://pith.science/pith/2BJFBU5CHZ44DBHSGFA52PX3JL/action/replication_record"}},"created_at":"2026-05-18T04:41:16.674678+00:00","updated_at":"2026-05-18T04:41:16.674678+00:00"}