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Tarieladze","submitted_at":"2012-06-04T11:40:02Z","abstract_excerpt":"A precompact group topology $\\tau$ on an abelian group $G$ is called {\\em single sequence characterized} (for short, {\\em ss-characterized}) if there is a sequence $\\mathbf{u}= (u_n)$ in $G$ such that $\\tau$ is the finest precompact group topology on $G$ making $\\mathbf{u}=(u_n)$ converge to zero. It is proved that a metrizable precompact abelian group $(G,\\tau)$ is $ss$-characterized iff it is countable. For every metrizable precompact group topology $\\tau$ on a countably infinite abelian group $G$ there exists a group topology $\\eta$ such that $\\eta$ is strictly finer than $\\tau$ and the gro"},"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":"1206.0587","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-06-04T11:40:02Z","cross_cats_sorted":[],"title_canon_sha256":"33f275c6f70a66dc5d7fc901c717be55117ee96a917d6227d71de83e8272543e","abstract_canon_sha256":"3588397b596ef63199fbae7372661ee052f1e22f6f6712edee3b41822b78f6e7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:54:17.183283Z","signature_b64":"PQNTxszS0FtiparRRNgUkaLtWCYJZBHDrUyrelgDuBdGq3NaqtLBJgz7PIuPwLhbhrVPtuBejSKML5mn9gSVCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bdccb40f57f206b17cc0539b6b5255756de829a495486b2e138f9577db306f64","last_reissued_at":"2026-05-18T03:54:17.182521Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:54:17.182521Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Characterizing sequences for precompact group topologies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"D. 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