{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:TJCB7L2A672DV54CAXQNCHLT22","short_pith_number":"pith:TJCB7L2A","schema_version":"1.0","canonical_sha256":"9a441faf40f7f43af78205e0d11d73d681a346508415fd70dda27786d03be861","source":{"kind":"arxiv","id":"1101.4615","version":1},"attestation_state":"computed","paper":{"title":"Variations of selective separability II: discrete sets and the influence of convergence and maximality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Angelo Bella, Mikhail Matveev, Santi Spadaro","submitted_at":"2011-01-24T18:26:58Z","abstract_excerpt":"A space $X$ is called selectively separable(R-separable) if for every sequence of dense subspaces $(D_n : n\\in\\omega)$ one can pick finite (respectively, one-point) subsets $F_n\\subset D_n$ such that $\\bigcup_{n\\in\\omega}F_n$ is dense in $X$. These properties are much stronger than separability, but are equivalent to it in the presence of certain convergence properties. For example, we show that every Hausdorff separable radial space is R-separable and note that neither separable sequential nor separable Whyburn spaces have to be selectively separable. A space is called \\emph{d-separable} if i"},"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":"1101.4615","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2011-01-24T18:26:58Z","cross_cats_sorted":[],"title_canon_sha256":"9d829d17639681ca4f3b1bfc80249393af2d31c22067eeccb0c2e1735f05de07","abstract_canon_sha256":"65ba866785e9326aa955d961a1a5afa73facabf38bb47ee5285a825af20622ec"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:06:46.249288Z","signature_b64":"kRFQ5vIiWTZrYAm8PAhra5GXfh3Q+92YvEw16rOMAejPw6feGR37EqH9fH+rFLemtvuvCZtMDARt5JHD69sLDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a441faf40f7f43af78205e0d11d73d681a346508415fd70dda27786d03be861","last_reissued_at":"2026-05-18T04:06:46.248715Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:06:46.248715Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Variations of selective separability II: discrete sets and the influence of convergence and maximality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Angelo Bella, Mikhail Matveev, Santi Spadaro","submitted_at":"2011-01-24T18:26:58Z","abstract_excerpt":"A space $X$ is called selectively separable(R-separable) if for every sequence of dense subspaces $(D_n : n\\in\\omega)$ one can pick finite (respectively, one-point) subsets $F_n\\subset D_n$ such that $\\bigcup_{n\\in\\omega}F_n$ is dense in $X$. These properties are much stronger than separability, but are equivalent to it in the presence of certain convergence properties. For example, we show that every Hausdorff separable radial space is R-separable and note that neither separable sequential nor separable Whyburn spaces have to be selectively separable. A space is called \\emph{d-separable} if i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.4615","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":"1101.4615","created_at":"2026-05-18T04:06:46.248807+00:00"},{"alias_kind":"arxiv_version","alias_value":"1101.4615v1","created_at":"2026-05-18T04:06:46.248807+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.4615","created_at":"2026-05-18T04:06:46.248807+00:00"},{"alias_kind":"pith_short_12","alias_value":"TJCB7L2A672D","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_16","alias_value":"TJCB7L2A672DV54C","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_8","alias_value":"TJCB7L2A","created_at":"2026-05-18T12:26:42.757692+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/TJCB7L2A672DV54CAXQNCHLT22","json":"https://pith.science/pith/TJCB7L2A672DV54CAXQNCHLT22.json","graph_json":"https://pith.science/api/pith-number/TJCB7L2A672DV54CAXQNCHLT22/graph.json","events_json":"https://pith.science/api/pith-number/TJCB7L2A672DV54CAXQNCHLT22/events.json","paper":"https://pith.science/paper/TJCB7L2A"},"agent_actions":{"view_html":"https://pith.science/pith/TJCB7L2A672DV54CAXQNCHLT22","download_json":"https://pith.science/pith/TJCB7L2A672DV54CAXQNCHLT22.json","view_paper":"https://pith.science/paper/TJCB7L2A","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1101.4615&json=true","fetch_graph":"https://pith.science/api/pith-number/TJCB7L2A672DV54CAXQNCHLT22/graph.json","fetch_events":"https://pith.science/api/pith-number/TJCB7L2A672DV54CAXQNCHLT22/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TJCB7L2A672DV54CAXQNCHLT22/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TJCB7L2A672DV54CAXQNCHLT22/action/storage_attestation","attest_author":"https://pith.science/pith/TJCB7L2A672DV54CAXQNCHLT22/action/author_attestation","sign_citation":"https://pith.science/pith/TJCB7L2A672DV54CAXQNCHLT22/action/citation_signature","submit_replication":"https://pith.science/pith/TJCB7L2A672DV54CAXQNCHLT22/action/replication_record"}},"created_at":"2026-05-18T04:06:46.248807+00:00","updated_at":"2026-05-18T04:06:46.248807+00:00"}