{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:CKL3G5GTB7SVERFNQ4C2UAG6OJ","short_pith_number":"pith:CKL3G5GT","schema_version":"1.0","canonical_sha256":"1297b374d30fe55244ad8705aa00de72611a793846aed50d42c68086b5892ef8","source":{"kind":"arxiv","id":"1412.1497","version":1},"attestation_state":"computed","paper":{"title":"On topological spaces and topological groups with certain local countable networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"J. Kakol, S. S. Gabriyelyan","submitted_at":"2014-12-03T21:30:11Z","abstract_excerpt":"Being motivated by the study of the space $C_c(X)$ of all continuous real-valued functions on a Tychonoff space $X$ with the compact-open topology, we introduced in [15] the concepts of a $cp$-network and a $cn$-network (at a point $x$) in $X$. In the present paper we describe the topology of $X$ admitting a countable $cp$- or $cn$-network at a point $x\\in X$. This description applies to provide new results about the strong Pytkeev property, already well recognized and applicable concept originally introduced by Tsaban and Zdomskyy [43]. We show that a Baire topological group $G$ is metrizable"},"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":"1412.1497","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2014-12-03T21:30:11Z","cross_cats_sorted":[],"title_canon_sha256":"e6f1edbd77abb2c6cfe3b7a03da9bd9c7389b7ccb06d0468887a94b2595a62d6","abstract_canon_sha256":"1a00badb727230ffe20cbe4a3b32bd6a932fa3aab633fabe60adb79f70a57806"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:07.070264Z","signature_b64":"JIHvezoC1dxGKSVZZuiRKF5Pq7idbjM16vp2ozK5IhZTVLYAKfLQCQ7VrDi4cHdQXdCE0Wf2mRvzgkmY1Mi7Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1297b374d30fe55244ad8705aa00de72611a793846aed50d42c68086b5892ef8","last_reissued_at":"2026-05-18T02:32:07.069904Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:07.069904Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On topological spaces and topological groups with certain local countable networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"J. Kakol, S. S. Gabriyelyan","submitted_at":"2014-12-03T21:30:11Z","abstract_excerpt":"Being motivated by the study of the space $C_c(X)$ of all continuous real-valued functions on a Tychonoff space $X$ with the compact-open topology, we introduced in [15] the concepts of a $cp$-network and a $cn$-network (at a point $x$) in $X$. In the present paper we describe the topology of $X$ admitting a countable $cp$- or $cn$-network at a point $x\\in X$. This description applies to provide new results about the strong Pytkeev property, already well recognized and applicable concept originally introduced by Tsaban and Zdomskyy [43]. We show that a Baire topological group $G$ is metrizable"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1497","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":"1412.1497","created_at":"2026-05-18T02:32:07.069958+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.1497v1","created_at":"2026-05-18T02:32:07.069958+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.1497","created_at":"2026-05-18T02:32:07.069958+00:00"},{"alias_kind":"pith_short_12","alias_value":"CKL3G5GTB7SV","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_16","alias_value":"CKL3G5GTB7SVERFN","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_8","alias_value":"CKL3G5GT","created_at":"2026-05-18T12:28:22.404517+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/CKL3G5GTB7SVERFNQ4C2UAG6OJ","json":"https://pith.science/pith/CKL3G5GTB7SVERFNQ4C2UAG6OJ.json","graph_json":"https://pith.science/api/pith-number/CKL3G5GTB7SVERFNQ4C2UAG6OJ/graph.json","events_json":"https://pith.science/api/pith-number/CKL3G5GTB7SVERFNQ4C2UAG6OJ/events.json","paper":"https://pith.science/paper/CKL3G5GT"},"agent_actions":{"view_html":"https://pith.science/pith/CKL3G5GTB7SVERFNQ4C2UAG6OJ","download_json":"https://pith.science/pith/CKL3G5GTB7SVERFNQ4C2UAG6OJ.json","view_paper":"https://pith.science/paper/CKL3G5GT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.1497&json=true","fetch_graph":"https://pith.science/api/pith-number/CKL3G5GTB7SVERFNQ4C2UAG6OJ/graph.json","fetch_events":"https://pith.science/api/pith-number/CKL3G5GTB7SVERFNQ4C2UAG6OJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CKL3G5GTB7SVERFNQ4C2UAG6OJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CKL3G5GTB7SVERFNQ4C2UAG6OJ/action/storage_attestation","attest_author":"https://pith.science/pith/CKL3G5GTB7SVERFNQ4C2UAG6OJ/action/author_attestation","sign_citation":"https://pith.science/pith/CKL3G5GTB7SVERFNQ4C2UAG6OJ/action/citation_signature","submit_replication":"https://pith.science/pith/CKL3G5GTB7SVERFNQ4C2UAG6OJ/action/replication_record"}},"created_at":"2026-05-18T02:32:07.069958+00:00","updated_at":"2026-05-18T02:32:07.069958+00:00"}