{"id":"https://openalex.org/W2077501971","doi":"https://doi.org/10.1305/ndjfl/1012429720","title":"Dependent Choices and Weak Compactness","display_name":"Dependent Choices and Weak Compactness","publication_year":1999,"publication_date":"1999-10-01","ids":{"openalex":"https://openalex.org/W2077501971","doi":"https://doi.org/10.1305/ndjfl/1012429720","mag":"2077501971"},"language":"en","primary_location":{"id":"doi:10.1305/ndjfl/1012429720","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1012429720","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-40/issue-4/Dependent-Choices-and-Weak-Compactness/10.1305/ndjfl/1012429720.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-40/issue-4/Dependent-Choices-and-Weak-Compactness/10.1305/ndjfl/1012429720.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001262881","display_name":"Christian Delhomm\u00e9","orcid":"https://orcid.org/0000-0003-1335-4281"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Christian Delhomm\u00e9","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5078218882","display_name":"Marianne Morillon","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Marianne Morillon","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.20582019,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"40","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11545","display_name":"Advanced Banach Space Theory","score":0.9921000003814697,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9904000163078308,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/compact-space","display_name":"Compact space","score":0.8553673624992371},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7085223197937012},{"id":"https://openalex.org/keywords/unit-sphere","display_name":"Unit sphere","score":0.6846034526824951},{"id":"https://openalex.org/keywords/axiom-of-choice","display_name":"Axiom of choice","score":0.6094512939453125},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.5699788928031921},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5487594604492188},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5377009510993958},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.4770055115222931},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.4759799540042877},{"id":"https://openalex.org/keywords/uniformly-convex-space","display_name":"Uniformly convex space","score":0.4475270211696625},{"id":"https://openalex.org/keywords/convex-set","display_name":"Convex set","score":0.4147937595844269},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37441110610961914},{"id":"https://openalex.org/keywords/eberlein\u2013\u0161mulian-theorem","display_name":"Eberlein\u2013\u0160mulian theorem","score":0.3350295424461365},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.24897456169128418},{"id":"https://openalex.org/keywords/set-theory","display_name":"Set theory","score":0.2428940236568451},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1861954629421234},{"id":"https://openalex.org/keywords/lp-space","display_name":"Lp space","score":0.1208600103855133},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.08278346061706543},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06426909565925598}],"concepts":[{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.8553673624992371},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7085223197937012},{"id":"https://openalex.org/C191948623","wikidata":"https://www.wikidata.org/wiki/Q1307800","display_name":"Unit sphere","level":2,"score":0.6846034526824951},{"id":"https://openalex.org/C151797676","wikidata":"https://www.wikidata.org/wiki/Q179692","display_name":"Axiom of choice","level":4,"score":0.6094512939453125},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.5699788928031921},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5487594604492188},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5377009510993958},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.4770055115222931},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.4759799540042877},{"id":"https://openalex.org/C123413131","wikidata":"https://www.wikidata.org/wiki/Q847535","display_name":"Uniformly convex space","level":5,"score":0.4475270211696625},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.4147937595844269},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37441110610961914},{"id":"https://openalex.org/C184908153","wikidata":"https://www.wikidata.org/wiki/Q2226650","display_name":"Eberlein\u2013\u0160mulian theorem","level":4,"score":0.3350295424461365},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.24897456169128418},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.2428940236568451},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1861954629421234},{"id":"https://openalex.org/C172294467","wikidata":"https://www.wikidata.org/wiki/Q305936","display_name":"Lp space","level":3,"score":0.1208600103855133},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.08278346061706543},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06426909565925598},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1305/ndjfl/1012429720","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1012429720","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-40/issue-4/Dependent-Choices-and-Weak-Compactness/10.1305/ndjfl/1012429720.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.99.3119","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.99.3119","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www2.univ-reunion.fr/~mar/ndjfl.pdf","raw_type":"text"},{"id":"pmh:oai:CULeuclid:euclid.ndjfl/1012429720","is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.ndjfl/1012429720","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1305/ndjfl/1012429720","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1012429720","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-40/issue-4/Dependent-Choices-and-Weak-Compactness/10.1305/ndjfl/1012429720.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2077501971.pdf","grobid_xml":"https://content.openalex.org/works/W2077501971.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W1521379649","https://openalex.org/W1541012876","https://openalex.org/W1608084331","https://openalex.org/W1978911266","https://openalex.org/W2092528704"],"related_works":["https://openalex.org/W2360424850","https://openalex.org/W1488344036","https://openalex.org/W2394473543","https://openalex.org/W2065449105","https://openalex.org/W2963620847","https://openalex.org/W2011557173","https://openalex.org/W2198155642","https://openalex.org/W2364998190","https://openalex.org/W2160018650","https://openalex.org/W749531014"],"abstract_inverted_index":{"We":[0,11],"work":[1],"in":[2,36,55],"set":[3],"theory":[4],"without":[5],"the":[6,14,22,39,58,71],"Axiom":[7],"of":[8,16,26,43,75],"Choice":[9],"ZF.":[10],"prove":[12],"that":[13,21,38,70],"Principle":[15],"Dependent":[17],"Choices":[18],"(DC)":[19],"implies":[20],"closed":[23,40,72],"unit":[24,41,73],"ball":[25,42,74],"a":[27,44,76],"uniformly":[28],"convex":[29],"Banach":[30],"space":[31,46,78],"is":[32,47,79],"weakly":[33,48,80],"compact":[34],"and,":[35],"particular,":[37],"Hilbert":[45],"compact.":[49,81],"These":[50],"statements":[51],"are":[52],"not":[53,62,68],"provable":[54],"ZF":[56],"and":[57],"latter":[59],"statement":[60],"does":[61,67],"imply":[63,69],"DC.":[64],"Furthermore,":[65],"DC":[66],"reflexive":[77]},"counts_by_year":[],"updated_date":"2026-08-11T07:18:39.950985","created_date":"2025-10-10T00:00:00"}
