{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:74DKJNWGE7SUPVETWMYVNRK2NP","short_pith_number":"pith:74DKJNWG","schema_version":"1.0","canonical_sha256":"ff06a4b6c627e547d493b33156c55a6bf2f4be6764d8970382929bc911ca7897","source":{"kind":"arxiv","id":"1705.07399","version":2},"attestation_state":"computed","paper":{"title":"Lower separation axioms via Borel and Baire algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Adam Barto\\v{s}, Taras Banakh","submitted_at":"2017-05-21T05:45:53Z","abstract_excerpt":"Let $\\kappa$ be an infinite regular cardinal. We define a topological space $X$ to be $T_{\\kappa-Borel}$-space (resp. a $T_{\\kappa-BP}$-space) if for every $x\\in X$ the singleton $\\{x\\}$ belongs to the smallest $\\kappa$-additive algebra of subsets of $X$ that contains all open sets (and all nowhere dense sets) in $X$. Each $T_1$-space is a $T_{\\kappa-Borel}$-space and each $T_{\\kappa-Borel}$-space is a $T_0$-space. On the other hand, $T_{\\kappa-BP}$-spaces need not be $T_0$-spaces.\n  We prove that a topological space $X$ is a $T_{\\kappa-Borel}$-space (resp. a $T_{\\kappa-BP}$-space) if and only"},"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":"1705.07399","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2017-05-21T05:45:53Z","cross_cats_sorted":[],"title_canon_sha256":"5668358a68bc096ece94d9f866003ddf2f81a0f2748a92fe0eddd636ab969338","abstract_canon_sha256":"837f46d25bfe54018fe4d291cb05ce6c287a029335ab607ea350ca9c7b3b321a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:11.347749Z","signature_b64":"FyJuYpvb0/SyEtzSqJdpesbk4DxD3DyxM+uNlqvGPQlLfxUsHdcCHzgzlFK6jOHYxfpDNvASRyxw/mfDb7XyCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ff06a4b6c627e547d493b33156c55a6bf2f4be6764d8970382929bc911ca7897","last_reissued_at":"2026-05-17T23:46:11.347401Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:11.347401Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lower separation axioms via Borel and Baire algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Adam Barto\\v{s}, Taras Banakh","submitted_at":"2017-05-21T05:45:53Z","abstract_excerpt":"Let $\\kappa$ be an infinite regular cardinal. We define a topological space $X$ to be $T_{\\kappa-Borel}$-space (resp. a $T_{\\kappa-BP}$-space) if for every $x\\in X$ the singleton $\\{x\\}$ belongs to the smallest $\\kappa$-additive algebra of subsets of $X$ that contains all open sets (and all nowhere dense sets) in $X$. Each $T_1$-space is a $T_{\\kappa-Borel}$-space and each $T_{\\kappa-Borel}$-space is a $T_0$-space. On the other hand, $T_{\\kappa-BP}$-spaces need not be $T_0$-spaces.\n  We prove that a topological space $X$ is a $T_{\\kappa-Borel}$-space (resp. a $T_{\\kappa-BP}$-space) if and only"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.07399","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":"1705.07399","created_at":"2026-05-17T23:46:11.347451+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.07399v2","created_at":"2026-05-17T23:46:11.347451+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.07399","created_at":"2026-05-17T23:46:11.347451+00:00"},{"alias_kind":"pith_short_12","alias_value":"74DKJNWGE7SU","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_16","alias_value":"74DKJNWGE7SUPVET","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_8","alias_value":"74DKJNWG","created_at":"2026-05-18T12:31:03.183658+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/74DKJNWGE7SUPVETWMYVNRK2NP","json":"https://pith.science/pith/74DKJNWGE7SUPVETWMYVNRK2NP.json","graph_json":"https://pith.science/api/pith-number/74DKJNWGE7SUPVETWMYVNRK2NP/graph.json","events_json":"https://pith.science/api/pith-number/74DKJNWGE7SUPVETWMYVNRK2NP/events.json","paper":"https://pith.science/paper/74DKJNWG"},"agent_actions":{"view_html":"https://pith.science/pith/74DKJNWGE7SUPVETWMYVNRK2NP","download_json":"https://pith.science/pith/74DKJNWGE7SUPVETWMYVNRK2NP.json","view_paper":"https://pith.science/paper/74DKJNWG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.07399&json=true","fetch_graph":"https://pith.science/api/pith-number/74DKJNWGE7SUPVETWMYVNRK2NP/graph.json","fetch_events":"https://pith.science/api/pith-number/74DKJNWGE7SUPVETWMYVNRK2NP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/74DKJNWGE7SUPVETWMYVNRK2NP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/74DKJNWGE7SUPVETWMYVNRK2NP/action/storage_attestation","attest_author":"https://pith.science/pith/74DKJNWGE7SUPVETWMYVNRK2NP/action/author_attestation","sign_citation":"https://pith.science/pith/74DKJNWGE7SUPVETWMYVNRK2NP/action/citation_signature","submit_replication":"https://pith.science/pith/74DKJNWGE7SUPVETWMYVNRK2NP/action/replication_record"}},"created_at":"2026-05-17T23:46:11.347451+00:00","updated_at":"2026-05-17T23:46:11.347451+00:00"}