{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:MZK7VOO5ZUSFSGGVG35SB53ISW","short_pith_number":"pith:MZK7VOO5","schema_version":"1.0","canonical_sha256":"6655fab9ddcd245918d536fb20f76895903c29c9e900d20546010217129af7e7","source":{"kind":"arxiv","id":"1504.04198","version":2},"attestation_state":"computed","paper":{"title":"Topological properties of function spaces $C_k(X,2)$ over zero-dimensional metric spaces $X$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.FA","authors_text":"S. Gabriyelyan","submitted_at":"2015-04-16T12:06:26Z","abstract_excerpt":"Let $X$ be a zero-dimensional metric space and $X'$ its derived set. We prove the following assertions: (1) the space $C_k(X,2)$ is an Ascoli space iff $C_k(X,2)$ is $k_\\mathbb{R}$-space iff either $X$ is locally compact or $X$ is not locally compact but $X'$ is compact, (2) $C_k(X,2)$ is a $k$-space iff either $X$ is a topological sum of a Polish locally compact space and a discrete space or $X$ is not locally compact but $X'$ is compact, (3) $C_k(X,2)$ is a sequential space iff $X$ is a Polish space and either $X$ is locally compact or $X$ is not locally compact but $X'$ is compact, (4) $C_k"},"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":"1504.04198","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-04-16T12:06:26Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"5f7cc85e59c50c7ec179efff42a4dc2294b04bdb74a97e9bbd1610bb6073b0bd","abstract_canon_sha256":"cc2c3e20cfd2d2bbe2e96b2aaebd00199ea574d922fad5e70ea1ec8404861a3d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:14.942620Z","signature_b64":"e3TVrGlxIN6XLsLLN1eTwUuNMXw4xsTnFayr8kQb51nDgu5n+t35TTTF8Nk6tjgV29Q+DL0KYz+EO+bCvwhRDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6655fab9ddcd245918d536fb20f76895903c29c9e900d20546010217129af7e7","last_reissued_at":"2026-05-18T02:18:14.941907Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:14.941907Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Topological properties of function spaces $C_k(X,2)$ over zero-dimensional metric spaces $X$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.FA","authors_text":"S. Gabriyelyan","submitted_at":"2015-04-16T12:06:26Z","abstract_excerpt":"Let $X$ be a zero-dimensional metric space and $X'$ its derived set. We prove the following assertions: (1) the space $C_k(X,2)$ is an Ascoli space iff $C_k(X,2)$ is $k_\\mathbb{R}$-space iff either $X$ is locally compact or $X$ is not locally compact but $X'$ is compact, (2) $C_k(X,2)$ is a $k$-space iff either $X$ is a topological sum of a Polish locally compact space and a discrete space or $X$ is not locally compact but $X'$ is compact, (3) $C_k(X,2)$ is a sequential space iff $X$ is a Polish space and either $X$ is locally compact or $X$ is not locally compact but $X'$ is compact, (4) $C_k"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04198","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":"1504.04198","created_at":"2026-05-18T02:18:14.942001+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.04198v2","created_at":"2026-05-18T02:18:14.942001+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.04198","created_at":"2026-05-18T02:18:14.942001+00:00"},{"alias_kind":"pith_short_12","alias_value":"MZK7VOO5ZUSF","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_16","alias_value":"MZK7VOO5ZUSFSGGV","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_8","alias_value":"MZK7VOO5","created_at":"2026-05-18T12:29:32.376354+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/MZK7VOO5ZUSFSGGVG35SB53ISW","json":"https://pith.science/pith/MZK7VOO5ZUSFSGGVG35SB53ISW.json","graph_json":"https://pith.science/api/pith-number/MZK7VOO5ZUSFSGGVG35SB53ISW/graph.json","events_json":"https://pith.science/api/pith-number/MZK7VOO5ZUSFSGGVG35SB53ISW/events.json","paper":"https://pith.science/paper/MZK7VOO5"},"agent_actions":{"view_html":"https://pith.science/pith/MZK7VOO5ZUSFSGGVG35SB53ISW","download_json":"https://pith.science/pith/MZK7VOO5ZUSFSGGVG35SB53ISW.json","view_paper":"https://pith.science/paper/MZK7VOO5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.04198&json=true","fetch_graph":"https://pith.science/api/pith-number/MZK7VOO5ZUSFSGGVG35SB53ISW/graph.json","fetch_events":"https://pith.science/api/pith-number/MZK7VOO5ZUSFSGGVG35SB53ISW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MZK7VOO5ZUSFSGGVG35SB53ISW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MZK7VOO5ZUSFSGGVG35SB53ISW/action/storage_attestation","attest_author":"https://pith.science/pith/MZK7VOO5ZUSFSGGVG35SB53ISW/action/author_attestation","sign_citation":"https://pith.science/pith/MZK7VOO5ZUSFSGGVG35SB53ISW/action/citation_signature","submit_replication":"https://pith.science/pith/MZK7VOO5ZUSFSGGVG35SB53ISW/action/replication_record"}},"created_at":"2026-05-18T02:18:14.942001+00:00","updated_at":"2026-05-18T02:18:14.942001+00:00"}