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We prove that any Taimanov semigroup $T$ has the following topological properties: (i) each $T_1$-topology with continuous shifts on $T$ is discrete; (ii) $T$ is closed in each $T_1$-topological semigroup containing $T$ as a subsemigroup; (iii) every non-isomorphic homomorphic image $Z$ of $T$ is a zero-semigroup and hence $Z$ is a topological semigroup in any topology on $Z$."},"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":"1612.08677","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-12-27T16:55:36Z","cross_cats_sorted":[],"title_canon_sha256":"e5301be09c144dc3c17fdfb2cc9c75469fc59fa3ced01c170caffe830f664cb6","abstract_canon_sha256":"14bcac4c774f9a14b053a220e255fa9b07e63d795650b2beb9e479b4467f405f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:03.655078Z","signature_b64":"+SeI00cLp4W0IZgwq+dnvOTT4p6AkTFX37x1cEQOcTs2I3OXAaO1ttBFn5kJS7DFAVFw6n9V/avR/Ptd878DAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e37cd3d5ab5613cdc64ea01e418df1171b7310bf172e7bf14e867c7f46e9492f","last_reissued_at":"2026-05-18T00:52:03.654605Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:03.654605Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Topological properties of Taimanov semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Oleg Gutik","submitted_at":"2016-12-27T16:55:36Z","abstract_excerpt":"A semigroup $T$ is called Taimanov if $T$ contains two distinct elements $0,\\infty$ such that $xy=\\infty$ for any distinct points $x,y\\in T\\setminus\\{0,\\infty\\}$ and $xy=0$ in all other cases. We prove that any Taimanov semigroup $T$ has the following topological properties: (i) each $T_1$-topology with continuous shifts on $T$ is discrete; (ii) $T$ is closed in each $T_1$-topological semigroup containing $T$ as a subsemigroup; (iii) every non-isomorphic homomorphic image $Z$ of $T$ is a zero-semigroup and hence $Z$ is a topological semigroup in any topology on $Z$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.08677","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":"1612.08677","created_at":"2026-05-18T00:52:03.654678+00:00"},{"alias_kind":"arxiv_version","alias_value":"1612.08677v2","created_at":"2026-05-18T00:52:03.654678+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.08677","created_at":"2026-05-18T00:52:03.654678+00:00"},{"alias_kind":"pith_short_12","alias_value":"4N6NHVNLKYJ4","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_16","alias_value":"4N6NHVNLKYJ43RSO","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_8","alias_value":"4N6NHVNL","created_at":"2026-05-18T12:29:58.707656+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/4N6NHVNLKYJ43RSOUAPEDDPRC4","json":"https://pith.science/pith/4N6NHVNLKYJ43RSOUAPEDDPRC4.json","graph_json":"https://pith.science/api/pith-number/4N6NHVNLKYJ43RSOUAPEDDPRC4/graph.json","events_json":"https://pith.science/api/pith-number/4N6NHVNLKYJ43RSOUAPEDDPRC4/events.json","paper":"https://pith.science/paper/4N6NHVNL"},"agent_actions":{"view_html":"https://pith.science/pith/4N6NHVNLKYJ43RSOUAPEDDPRC4","download_json":"https://pith.science/pith/4N6NHVNLKYJ43RSOUAPEDDPRC4.json","view_paper":"https://pith.science/paper/4N6NHVNL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1612.08677&json=true","fetch_graph":"https://pith.science/api/pith-number/4N6NHVNLKYJ43RSOUAPEDDPRC4/graph.json","fetch_events":"https://pith.science/api/pith-number/4N6NHVNLKYJ43RSOUAPEDDPRC4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4N6NHVNLKYJ43RSOUAPEDDPRC4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4N6NHVNLKYJ43RSOUAPEDDPRC4/action/storage_attestation","attest_author":"https://pith.science/pith/4N6NHVNLKYJ43RSOUAPEDDPRC4/action/author_attestation","sign_citation":"https://pith.science/pith/4N6NHVNLKYJ43RSOUAPEDDPRC4/action/citation_signature","submit_replication":"https://pith.science/pith/4N6NHVNLKYJ43RSOUAPEDDPRC4/action/replication_record"}},"created_at":"2026-05-18T00:52:03.654678+00:00","updated_at":"2026-05-18T00:52:03.654678+00:00"}