{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:SJ5VKE3BYB7NET4ZYKNB522OA4","short_pith_number":"pith:SJ5VKE3B","schema_version":"1.0","canonical_sha256":"927b551361c07ed24f99c29a1eeb4e0701529e7fae3103355f362aef21286f6a","source":{"kind":"arxiv","id":"1810.05390","version":1},"attestation_state":"computed","paper":{"title":"New separation axioms in generalized bitopological spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Amar Kumar Banerjee, Jagannath Pal","submitted_at":"2018-10-12T07:52:59Z","abstract_excerpt":"Here we have studied on the ideas of $g_{\\mu_i}$ and $\\lambda_{\\mu_i}$-closed sets with respect to ${\\mu_j}(i,j=1,2,i\\not=j)$ and pairwise $ \\lambda $-closed sets in a generalized bitopological space $ (X,\\mu_1, \\mu_2) $. We have also investigated the properties on some new separation axioms namely pairwise $ T_\\frac{1}{4}$, pairwise $T_\\frac{3}{8}$, pairwise $ T_\\frac{5}{8} $ and have established their mutual relations with pairwise $ T_0 $, pairwise $ T_\\frac{1}{2} $ and pairwise $ T_1 $. We have also shown that under certain conditions these axioms are equivalent."},"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":"1810.05390","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2018-10-12T07:52:59Z","cross_cats_sorted":[],"title_canon_sha256":"bd98ad62a7c4f2a55160ec2d8172734b419555405ac4ce2e53fe3e93539f9960","abstract_canon_sha256":"020b0710a4e21d422141a3a730f817ce7617afbab1b9905059d33843ddfc8bd6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:30.760778Z","signature_b64":"pCw1E1EsXG27xsjG2SZqd/zPt5YNwQZb1oTJ/7lJW/in+oz19o5INbQTHGluiuF+HNPmZEWDd1d3WHXcf3IlCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"927b551361c07ed24f99c29a1eeb4e0701529e7fae3103355f362aef21286f6a","last_reissued_at":"2026-05-18T00:03:30.760049Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:30.760049Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"New separation axioms in generalized bitopological spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Amar Kumar Banerjee, Jagannath Pal","submitted_at":"2018-10-12T07:52:59Z","abstract_excerpt":"Here we have studied on the ideas of $g_{\\mu_i}$ and $\\lambda_{\\mu_i}$-closed sets with respect to ${\\mu_j}(i,j=1,2,i\\not=j)$ and pairwise $ \\lambda $-closed sets in a generalized bitopological space $ (X,\\mu_1, \\mu_2) $. We have also investigated the properties on some new separation axioms namely pairwise $ T_\\frac{1}{4}$, pairwise $T_\\frac{3}{8}$, pairwise $ T_\\frac{5}{8} $ and have established their mutual relations with pairwise $ T_0 $, pairwise $ T_\\frac{1}{2} $ and pairwise $ T_1 $. We have also shown that under certain conditions these axioms are equivalent."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.05390","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":"1810.05390","created_at":"2026-05-18T00:03:30.760166+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.05390v1","created_at":"2026-05-18T00:03:30.760166+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.05390","created_at":"2026-05-18T00:03:30.760166+00:00"},{"alias_kind":"pith_short_12","alias_value":"SJ5VKE3BYB7N","created_at":"2026-05-18T12:32:53.628368+00:00"},{"alias_kind":"pith_short_16","alias_value":"SJ5VKE3BYB7NET4Z","created_at":"2026-05-18T12:32:53.628368+00:00"},{"alias_kind":"pith_short_8","alias_value":"SJ5VKE3B","created_at":"2026-05-18T12:32:53.628368+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/SJ5VKE3BYB7NET4ZYKNB522OA4","json":"https://pith.science/pith/SJ5VKE3BYB7NET4ZYKNB522OA4.json","graph_json":"https://pith.science/api/pith-number/SJ5VKE3BYB7NET4ZYKNB522OA4/graph.json","events_json":"https://pith.science/api/pith-number/SJ5VKE3BYB7NET4ZYKNB522OA4/events.json","paper":"https://pith.science/paper/SJ5VKE3B"},"agent_actions":{"view_html":"https://pith.science/pith/SJ5VKE3BYB7NET4ZYKNB522OA4","download_json":"https://pith.science/pith/SJ5VKE3BYB7NET4ZYKNB522OA4.json","view_paper":"https://pith.science/paper/SJ5VKE3B","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.05390&json=true","fetch_graph":"https://pith.science/api/pith-number/SJ5VKE3BYB7NET4ZYKNB522OA4/graph.json","fetch_events":"https://pith.science/api/pith-number/SJ5VKE3BYB7NET4ZYKNB522OA4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SJ5VKE3BYB7NET4ZYKNB522OA4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SJ5VKE3BYB7NET4ZYKNB522OA4/action/storage_attestation","attest_author":"https://pith.science/pith/SJ5VKE3BYB7NET4ZYKNB522OA4/action/author_attestation","sign_citation":"https://pith.science/pith/SJ5VKE3BYB7NET4ZYKNB522OA4/action/citation_signature","submit_replication":"https://pith.science/pith/SJ5VKE3BYB7NET4ZYKNB522OA4/action/replication_record"}},"created_at":"2026-05-18T00:03:30.760166+00:00","updated_at":"2026-05-18T00:03:30.760166+00:00"}