{"id":"https://openalex.org/W1995975622","doi":"https://doi.org/10.2178/jsl/1190150035","title":"Definitions of compactness and the axiom of choice","display_name":"Definitions of compactness and the axiom of choice","publication_year":2002,"publication_date":"2002-03-01","ids":{"openalex":"https://openalex.org/W1995975622","doi":"https://doi.org/10.2178/jsl/1190150035","mag":"1995975622"},"language":"en","primary_location":{"id":"doi:10.2178/jsl/1190150035","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1190150035","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5028328758","display_name":"Omar De la Cruz","orcid":"https://orcid.org/0000-0001-9489-4647"},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Omar De La Cruz","raw_affiliation_strings":["Mathematics Department, Purdue University, West Lafayette, IN 47907, USA, E-mail:","Purdue University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Department, Purdue University, West Lafayette, IN 47907, USA, E-mail:","institution_ids":["https://openalex.org/I219193219"]},{"raw_affiliation_string":"Purdue University","institution_ids":["https://openalex.org/I219193219"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101476392","display_name":"Eric Hall","orcid":"https://orcid.org/0000-0001-6159-7494"},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Eric Hall","raw_affiliation_strings":["Mathematics Department, Purdue University, West Lafayette, IN 47907, USA, E-mail:","Purdue University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Department, Purdue University, West Lafayette, IN 47907, USA, E-mail:","institution_ids":["https://openalex.org/I219193219"]},{"raw_affiliation_string":"Purdue University","institution_ids":["https://openalex.org/I219193219"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108590548","display_name":"Paul C. Howard","orcid":null},"institutions":[{"id":"https://openalex.org/I138216421","display_name":"Eastern Michigan University","ror":"https://ror.org/02ehshm78","country_code":"US","type":"education","lineage":["https://openalex.org/I138216421"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Paul Howard","raw_affiliation_strings":["Mathematics Department, Eastern Michigan University, Yipsilanti, MI 48197, USA, E-mail:","Eastern Michigan University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Department, Eastern Michigan University, Yipsilanti, MI 48197, USA, E-mail:","institution_ids":["https://openalex.org/I138216421"]},{"raw_affiliation_string":"Eastern Michigan University","institution_ids":["https://openalex.org/I138216421"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073538536","display_name":"Jean E. Rubin","orcid":null},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jean E. Rubin","raw_affiliation_strings":["Mathematics Department, Purdue University, West Lafayette, IN 47907, USA, E-mail:","Purdue University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Department, Purdue University, West Lafayette, IN 47907, USA, E-mail:","institution_ids":["https://openalex.org/I219193219"]},{"raw_affiliation_string":"Purdue University","institution_ids":["https://openalex.org/I219193219"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018152831","display_name":"Adrienne Stanley","orcid":"https://orcid.org/0009-0005-3110-1335"},"institutions":[{"id":"https://openalex.org/I119234918","display_name":"University of Northern Iowa","ror":"https://ror.org/02h4qpx12","country_code":"US","type":"education","lineage":["https://openalex.org/I119234918"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Adrienne Stanley","raw_affiliation_strings":["Mathematics Department, University of Northern Iowa, Cedar Falls, IA 50614, USA, E-mail:","[University of Northern Iowa]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Department, University of Northern Iowa, Cedar Falls, IA 50614, USA, E-mail:","institution_ids":["https://openalex.org/I119234918"]},{"raw_affiliation_string":"[University of Northern Iowa]","institution_ids":["https://openalex.org/I119234918"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.1408,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.93123845,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":null,"biblio":{"volume":"67","issue":"1","first_page":"143","last_page":"161"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9988999962806702,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9883000254631042,"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":0.8922909498214722},{"id":"https://openalex.org/keywords/axiom-of-choice","display_name":"Axiom of choice","score":0.8480464220046997},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.7656142711639404},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5589113235473633},{"id":"https://openalex.org/keywords/axiom-independence","display_name":"Axiom independence","score":0.5076819658279419},{"id":"https://openalex.org/keywords/topological-space","display_name":"Topological space","score":0.4538981318473816},{"id":"https://openalex.org/keywords/urelement","display_name":"Urelement","score":0.44313064217567444},{"id":"https://openalex.org/keywords/zermelo\u2013fraenkel-set-theory","display_name":"Zermelo\u2013Fraenkel set theory","score":0.42848795652389526},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4180991053581238},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.4128163456916809},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2739105522632599},{"id":"https://openalex.org/keywords/set-theory","display_name":"Set theory","score":0.2572084069252014},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.24749261140823364},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.05992189049720764}],"concepts":[{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.8922909498214722},{"id":"https://openalex.org/C151797676","wikidata":"https://www.wikidata.org/wiki/Q179692","display_name":"Axiom of choice","level":4,"score":0.8480464220046997},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.7656142711639404},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5589113235473633},{"id":"https://openalex.org/C170088968","wikidata":"https://www.wikidata.org/wiki/Q4830547","display_name":"Axiom independence","level":3,"score":0.5076819658279419},{"id":"https://openalex.org/C81332173","wikidata":"https://www.wikidata.org/wiki/Q179899","display_name":"Topological space","level":2,"score":0.4538981318473816},{"id":"https://openalex.org/C78550038","wikidata":"https://www.wikidata.org/wiki/Q1896657","display_name":"Urelement","level":5,"score":0.44313064217567444},{"id":"https://openalex.org/C51460","wikidata":"https://www.wikidata.org/wiki/Q191849","display_name":"Zermelo\u2013Fraenkel set theory","level":5,"score":0.42848795652389526},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4180991053581238},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.4128163456916809},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2739105522632599},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.2572084069252014},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.24749261140823364},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.05992189049720764},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.2178/jsl/1190150035","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1190150035","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:scholarworks.uni.edu:facpub-4485","is_oa":false,"landing_page_url":"https://scholarworks.uni.edu/facpub/3484","pdf_url":null,"source":{"id":"https://openalex.org/S4377196489","display_name":"UNI ScholarWorks (University of Northern Iowa)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I119234918","host_organization_name":"University of Northern Iowa","host_organization_lineage":["https://openalex.org/I119234918"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Faculty Publications","raw_type":"text"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1190150035","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1190150035","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.84.8454","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.84.8454","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.purdue.edu/~jer/Papers/compactness.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.5799999833106995,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W4594304","https://openalex.org/W245573756","https://openalex.org/W998035377","https://openalex.org/W1541012876","https://openalex.org/W1608084331","https://openalex.org/W1968443233","https://openalex.org/W1983437996","https://openalex.org/W1991980065","https://openalex.org/W1998540768","https://openalex.org/W2022219040","https://openalex.org/W2051953527","https://openalex.org/W2070383345","https://openalex.org/W2084404970","https://openalex.org/W2326155258","https://openalex.org/W2334527086","https://openalex.org/W4230977178","https://openalex.org/W4233444413","https://openalex.org/W4245746908"],"related_works":["https://openalex.org/W288388583","https://openalex.org/W1995120876","https://openalex.org/W2491940682","https://openalex.org/W1504849543","https://openalex.org/W2350176099","https://openalex.org/W4254487684","https://openalex.org/W2017671599","https://openalex.org/W2076278624","https://openalex.org/W2796622564","https://openalex.org/W1999748057"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"study":[2],"the":[3,13,15],"relationships":[4],"between":[5],"definitions":[6],"of":[7,17],"compactness":[8],"in":[9,20],"topological":[10],"spaces":[11],"and":[12],"roll":[14],"axiom":[16],"choice":[18],"plays":[19],"these":[21],"relationships.":[22]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}