{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:YUYCQ2NQFPL3LMWVHEIQPRILZW","short_pith_number":"pith:YUYCQ2NQ","schema_version":"1.0","canonical_sha256":"c5302869b02bd7b5b2d5391107c50bcdb4168ade93a8a6e1306893cf435767b8","source":{"kind":"arxiv","id":"1809.06807","version":1},"attestation_state":"computed","paper":{"title":"Disconnectedness properties of Hyperspaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Angel Tamariz-Mascar\\'ua, Rodrigo Hern\\'andez-Guti\\'errez","submitted_at":"2018-09-18T16:00:10Z","abstract_excerpt":"Let $X$ be a Hausdorff space and let $\\mathcal{H}$ be one of the hyperspaces $CL(X)$, $\\mathcal{K}(X)$, $\\mathcal{F}(X)$ or $\\mathcal{F}_n(X)$ ($n$ a positive integer) with the Vietoris topology. We study the following disconnectedness properties for $\\mathcal{H}$: extremal disconnectedness, being a $F^\\prime$-space, $P$-space or weak $P$-space and hereditary disconnectedness. Our main result states: if $X$ is Hausdorff and $F\\subset X$ is a closed subset such that $(a)$ both $F$ and $X-F$ are totally disconnected, $(b)$ the quotient $X/F$ is hereditarily disconnected, then $\\mathcal{K}(X)$ is"},"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":"1809.06807","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2018-09-18T16:00:10Z","cross_cats_sorted":[],"title_canon_sha256":"666f8911e501a49abb391665e664dd29fce4964c4326351abfa46cf92d8f0726","abstract_canon_sha256":"a2731be9e7ef9c094b68dc0780b0fa9bb6b4d6c023079d2954158a14788467db"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:24.658840Z","signature_b64":"ZR2FaGmvXI6LwzNFZSU+0bh24GDPUNoUYTX9dQ5e3ontBWmGlndxDoF/HmhTyLUkXBi3KPi4pHDuSkVMqFotAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5302869b02bd7b5b2d5391107c50bcdb4168ade93a8a6e1306893cf435767b8","last_reissued_at":"2026-05-18T00:05:24.658216Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:24.658216Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Disconnectedness properties of Hyperspaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Angel Tamariz-Mascar\\'ua, Rodrigo Hern\\'andez-Guti\\'errez","submitted_at":"2018-09-18T16:00:10Z","abstract_excerpt":"Let $X$ be a Hausdorff space and let $\\mathcal{H}$ be one of the hyperspaces $CL(X)$, $\\mathcal{K}(X)$, $\\mathcal{F}(X)$ or $\\mathcal{F}_n(X)$ ($n$ a positive integer) with the Vietoris topology. We study the following disconnectedness properties for $\\mathcal{H}$: extremal disconnectedness, being a $F^\\prime$-space, $P$-space or weak $P$-space and hereditary disconnectedness. Our main result states: if $X$ is Hausdorff and $F\\subset X$ is a closed subset such that $(a)$ both $F$ and $X-F$ are totally disconnected, $(b)$ the quotient $X/F$ is hereditarily disconnected, then $\\mathcal{K}(X)$ is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.06807","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":"1809.06807","created_at":"2026-05-18T00:05:24.658306+00:00"},{"alias_kind":"arxiv_version","alias_value":"1809.06807v1","created_at":"2026-05-18T00:05:24.658306+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.06807","created_at":"2026-05-18T00:05:24.658306+00:00"},{"alias_kind":"pith_short_12","alias_value":"YUYCQ2NQFPL3","created_at":"2026-05-18T12:33:04.347982+00:00"},{"alias_kind":"pith_short_16","alias_value":"YUYCQ2NQFPL3LMWV","created_at":"2026-05-18T12:33:04.347982+00:00"},{"alias_kind":"pith_short_8","alias_value":"YUYCQ2NQ","created_at":"2026-05-18T12:33:04.347982+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/YUYCQ2NQFPL3LMWVHEIQPRILZW","json":"https://pith.science/pith/YUYCQ2NQFPL3LMWVHEIQPRILZW.json","graph_json":"https://pith.science/api/pith-number/YUYCQ2NQFPL3LMWVHEIQPRILZW/graph.json","events_json":"https://pith.science/api/pith-number/YUYCQ2NQFPL3LMWVHEIQPRILZW/events.json","paper":"https://pith.science/paper/YUYCQ2NQ"},"agent_actions":{"view_html":"https://pith.science/pith/YUYCQ2NQFPL3LMWVHEIQPRILZW","download_json":"https://pith.science/pith/YUYCQ2NQFPL3LMWVHEIQPRILZW.json","view_paper":"https://pith.science/paper/YUYCQ2NQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1809.06807&json=true","fetch_graph":"https://pith.science/api/pith-number/YUYCQ2NQFPL3LMWVHEIQPRILZW/graph.json","fetch_events":"https://pith.science/api/pith-number/YUYCQ2NQFPL3LMWVHEIQPRILZW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YUYCQ2NQFPL3LMWVHEIQPRILZW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YUYCQ2NQFPL3LMWVHEIQPRILZW/action/storage_attestation","attest_author":"https://pith.science/pith/YUYCQ2NQFPL3LMWVHEIQPRILZW/action/author_attestation","sign_citation":"https://pith.science/pith/YUYCQ2NQFPL3LMWVHEIQPRILZW/action/citation_signature","submit_replication":"https://pith.science/pith/YUYCQ2NQFPL3LMWVHEIQPRILZW/action/replication_record"}},"created_at":"2026-05-18T00:05:24.658306+00:00","updated_at":"2026-05-18T00:05:24.658306+00:00"}