{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2005:CJ7CPBP63BVEL3FEOEZVUAWBXX","short_pith_number":"pith:CJ7CPBP6","schema_version":"1.0","canonical_sha256":"127e2785fed86a45eca471335a02c1bdfc21b2b441daa5916812df39e7858240","source":{"kind":"arxiv","id":"math/0502223","version":2},"attestation_state":"computed","paper":{"title":"Precompact abelian groups and topological annihilators","license":"","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GN","authors_text":"G\\'abor Luk\\'acs","submitted_at":"2005-02-10T23:37:16Z","abstract_excerpt":"For a compact Hausdorff abelian group K and its subgroup H, one defines the g-closure g(H) of H in K as the subgroup consisting of $\\chi \\in K$ such that $\\chi(a_n)\\longrightarrow 0$ in T=R/Z for every sequence {a_n} in $\\hat K$ (the Pontryagin dual of K) that converges to 0 in the topology that H induces on $\\hat K$. We prove that every countable subgroup of a compact Hausdorff group is g-closed, and thus give a positive answer to two problems of Dikranjan, Milan and Tonolo. We also show that every g-closed subgroup of a compact Hausdorff group is realcompact. The techniques developed in the "},"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/0502223","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.GN","submitted_at":"2005-02-10T23:37:16Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"322ba5bc42c2b19b4a26e73c35b1302683505e9db67aaac04da10f6df62b3ceb","abstract_canon_sha256":"49fb95afbdccb90cbcf031c570cd01ab5cc0c6644f5c26dd6000515dd71a0ef6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:12:19.413420Z","signature_b64":"Mgt/zjQcnA4XzHFBDEtZGwsPDSUmRguvsjNAz/fX2AX+hgtf4i6+m1P+OO94PGwxbuJCH0xumEBnMpVH64V3CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"127e2785fed86a45eca471335a02c1bdfc21b2b441daa5916812df39e7858240","last_reissued_at":"2026-05-18T04:12:19.412741Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:12:19.412741Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Precompact abelian groups and topological annihilators","license":"","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GN","authors_text":"G\\'abor Luk\\'acs","submitted_at":"2005-02-10T23:37:16Z","abstract_excerpt":"For a compact Hausdorff abelian group K and its subgroup H, one defines the g-closure g(H) of H in K as the subgroup consisting of $\\chi \\in K$ such that $\\chi(a_n)\\longrightarrow 0$ in T=R/Z for every sequence {a_n} in $\\hat K$ (the Pontryagin dual of K) that converges to 0 in the topology that H induces on $\\hat K$. We prove that every countable subgroup of a compact Hausdorff group is g-closed, and thus give a positive answer to two problems of Dikranjan, Milan and Tonolo. We also show that every g-closed subgroup of a compact Hausdorff group is realcompact. The techniques developed in the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0502223","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":"math/0502223","created_at":"2026-05-18T04:12:19.412842+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0502223v2","created_at":"2026-05-18T04:12:19.412842+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0502223","created_at":"2026-05-18T04:12:19.412842+00:00"},{"alias_kind":"pith_short_12","alias_value":"CJ7CPBP63BVE","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_16","alias_value":"CJ7CPBP63BVEL3FE","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_8","alias_value":"CJ7CPBP6","created_at":"2026-05-18T12:25:53.335082+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/CJ7CPBP63BVEL3FEOEZVUAWBXX","json":"https://pith.science/pith/CJ7CPBP63BVEL3FEOEZVUAWBXX.json","graph_json":"https://pith.science/api/pith-number/CJ7CPBP63BVEL3FEOEZVUAWBXX/graph.json","events_json":"https://pith.science/api/pith-number/CJ7CPBP63BVEL3FEOEZVUAWBXX/events.json","paper":"https://pith.science/paper/CJ7CPBP6"},"agent_actions":{"view_html":"https://pith.science/pith/CJ7CPBP63BVEL3FEOEZVUAWBXX","download_json":"https://pith.science/pith/CJ7CPBP63BVEL3FEOEZVUAWBXX.json","view_paper":"https://pith.science/paper/CJ7CPBP6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0502223&json=true","fetch_graph":"https://pith.science/api/pith-number/CJ7CPBP63BVEL3FEOEZVUAWBXX/graph.json","fetch_events":"https://pith.science/api/pith-number/CJ7CPBP63BVEL3FEOEZVUAWBXX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CJ7CPBP63BVEL3FEOEZVUAWBXX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CJ7CPBP63BVEL3FEOEZVUAWBXX/action/storage_attestation","attest_author":"https://pith.science/pith/CJ7CPBP63BVEL3FEOEZVUAWBXX/action/author_attestation","sign_citation":"https://pith.science/pith/CJ7CPBP63BVEL3FEOEZVUAWBXX/action/citation_signature","submit_replication":"https://pith.science/pith/CJ7CPBP63BVEL3FEOEZVUAWBXX/action/replication_record"}},"created_at":"2026-05-18T04:12:19.412842+00:00","updated_at":"2026-05-18T04:12:19.412842+00:00"}