{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:4HNUG333IP2VMBCAU66CBR5DSC","short_pith_number":"pith:4HNUG333","schema_version":"1.0","canonical_sha256":"e1db436f7b43f5560440a7bc20c7a3909edf2e87c1f1ff8f80ee2927bf73cbfa","source":{"kind":"arxiv","id":"0811.4272","version":1},"attestation_state":"computed","paper":{"title":"Openly factorizable spaces and compact extensions of topological semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GN","authors_text":"Svetlana Dimitrova, Taras Banakh","submitted_at":"2008-11-26T11:22:05Z","abstract_excerpt":"We prove that the semigroup operation of a topological semigroup $S$ extends to a continuous semigroup operation on its the Stone-\\v{C}ech compactification $\\beta S$ provided $S$ is a pseudocompact openly factorizable space, which means that each map $f:S\\to Y$ to a second countable space $Y$ can be written as the composition $f=g\\circ p$ of an open map $p:X\\to Z$ onto a second countable space $Z$ and a map $g:Z\\to Y$. We present a spectral characterization of openly factorizable spaces and establish some properties of such spaces."},"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":"0811.4272","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2008-11-26T11:22:05Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"161ed5b32f02c421847f0a0c33ca6edaef47f4271685fbed921d499658217a09","abstract_canon_sha256":"52edbc2e29cc8e0f90b8d2af076c7e0b42dac610051c93d441a0c815798a9d34"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:11:29.240365Z","signature_b64":"/KcTF9X9hLJenVnPoKYN2cKfpBtBYNOmIUBkOZvT/9ftaobb48mYWdP9vy9JYGhJVz/iRJ/GVe/lsiKLtB5rBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e1db436f7b43f5560440a7bc20c7a3909edf2e87c1f1ff8f80ee2927bf73cbfa","last_reissued_at":"2026-05-18T04:11:29.239626Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:11:29.239626Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Openly factorizable spaces and compact extensions of topological semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GN","authors_text":"Svetlana Dimitrova, Taras Banakh","submitted_at":"2008-11-26T11:22:05Z","abstract_excerpt":"We prove that the semigroup operation of a topological semigroup $S$ extends to a continuous semigroup operation on its the Stone-\\v{C}ech compactification $\\beta S$ provided $S$ is a pseudocompact openly factorizable space, which means that each map $f:S\\to Y$ to a second countable space $Y$ can be written as the composition $f=g\\circ p$ of an open map $p:X\\to Z$ onto a second countable space $Z$ and a map $g:Z\\to Y$. We present a spectral characterization of openly factorizable spaces and establish some properties of such spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.4272","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":"0811.4272","created_at":"2026-05-18T04:11:29.239743+00:00"},{"alias_kind":"arxiv_version","alias_value":"0811.4272v1","created_at":"2026-05-18T04:11:29.239743+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0811.4272","created_at":"2026-05-18T04:11:29.239743+00:00"},{"alias_kind":"pith_short_12","alias_value":"4HNUG333IP2V","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_16","alias_value":"4HNUG333IP2VMBCA","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_8","alias_value":"4HNUG333","created_at":"2026-05-18T12:25:56.245647+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/4HNUG333IP2VMBCAU66CBR5DSC","json":"https://pith.science/pith/4HNUG333IP2VMBCAU66CBR5DSC.json","graph_json":"https://pith.science/api/pith-number/4HNUG333IP2VMBCAU66CBR5DSC/graph.json","events_json":"https://pith.science/api/pith-number/4HNUG333IP2VMBCAU66CBR5DSC/events.json","paper":"https://pith.science/paper/4HNUG333"},"agent_actions":{"view_html":"https://pith.science/pith/4HNUG333IP2VMBCAU66CBR5DSC","download_json":"https://pith.science/pith/4HNUG333IP2VMBCAU66CBR5DSC.json","view_paper":"https://pith.science/paper/4HNUG333","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0811.4272&json=true","fetch_graph":"https://pith.science/api/pith-number/4HNUG333IP2VMBCAU66CBR5DSC/graph.json","fetch_events":"https://pith.science/api/pith-number/4HNUG333IP2VMBCAU66CBR5DSC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4HNUG333IP2VMBCAU66CBR5DSC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4HNUG333IP2VMBCAU66CBR5DSC/action/storage_attestation","attest_author":"https://pith.science/pith/4HNUG333IP2VMBCAU66CBR5DSC/action/author_attestation","sign_citation":"https://pith.science/pith/4HNUG333IP2VMBCAU66CBR5DSC/action/citation_signature","submit_replication":"https://pith.science/pith/4HNUG333IP2VMBCAU66CBR5DSC/action/replication_record"}},"created_at":"2026-05-18T04:11:29.239743+00:00","updated_at":"2026-05-18T04:11:29.239743+00:00"}