{"id":"https://openalex.org/W1990165314","doi":"https://doi.org/10.1305/ndjfl/1093870373","title":"The axiom of choice in topology.","display_name":"The axiom of choice in topology.","publication_year":1983,"publication_date":"1983-07-01","ids":{"openalex":"https://openalex.org/W1990165314","doi":"https://doi.org/10.1305/ndjfl/1093870373","mag":"1990165314"},"language":"en","primary_location":{"id":"doi:10.1305/ndjfl/1093870373","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093870373","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-24/issue-3/The-axiom-of-choice-in-topology/10.1305/ndjfl/1093870373.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-24/issue-3/The-axiom-of-choice-in-topology/10.1305/ndjfl/1093870373.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034039240","display_name":"Norbert Brunner","orcid":"https://orcid.org/0000-0001-6487-5752"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Norbert Brunner","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5034039240"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.3718,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.88997843,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"24","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.2071000039577484,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.2071000039577484,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.1809999942779541,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/axiom-of-choice","display_name":"Axiom of choice","score":0.8906902074813843},{"id":"https://openalex.org/keywords/constructive-set-theory","display_name":"Constructive set theory","score":0.7874755859375},{"id":"https://openalex.org/keywords/urelement","display_name":"Urelement","score":0.7642528414726257},{"id":"https://openalex.org/keywords/zermelo\u2013fraenkel-set-theory","display_name":"Zermelo\u2013Fraenkel set theory","score":0.7054377794265747},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.5512637495994568},{"id":"https://openalex.org/keywords/axiom-independence","display_name":"Axiom independence","score":0.5176227688789368},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4937301576137543},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.48715636134147644},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4217960238456726},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.34495076537132263},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32865023612976074},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.22846010327339172},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.09063789248466492},{"id":"https://openalex.org/keywords/set-theory","display_name":"Set theory","score":0.08064424991607666},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07332906126976013}],"concepts":[{"id":"https://openalex.org/C151797676","wikidata":"https://www.wikidata.org/wiki/Q179692","display_name":"Axiom of choice","level":4,"score":0.8906902074813843},{"id":"https://openalex.org/C556429856","wikidata":"https://www.wikidata.org/wiki/Q5164501","display_name":"Constructive set theory","level":5,"score":0.7874755859375},{"id":"https://openalex.org/C78550038","wikidata":"https://www.wikidata.org/wiki/Q1896657","display_name":"Urelement","level":5,"score":0.7642528414726257},{"id":"https://openalex.org/C51460","wikidata":"https://www.wikidata.org/wiki/Q191849","display_name":"Zermelo\u2013Fraenkel set theory","level":5,"score":0.7054377794265747},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.5512637495994568},{"id":"https://openalex.org/C170088968","wikidata":"https://www.wikidata.org/wiki/Q4830547","display_name":"Axiom independence","level":3,"score":0.5176227688789368},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4937301576137543},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.48715636134147644},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4217960238456726},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.34495076537132263},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32865023612976074},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.22846010327339172},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.09063789248466492},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.08064424991607666},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07332906126976013},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1305/ndjfl/1093870373","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093870373","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-24/issue-3/The-axiom-of-choice-in-topology/10.1305/ndjfl/1093870373.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:CULeuclid:euclid.ndjfl/1093870373","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.ndjfl/1093870373","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/1093870373","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093870373","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-24/issue-3/The-axiom-of-choice-in-topology/10.1305/ndjfl/1093870373.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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1990165314.pdf","grobid_xml":"https://content.openalex.org/works/W1990165314.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W4111744","https://openalex.org/W328650061","https://openalex.org/W655855359","https://openalex.org/W904001724","https://openalex.org/W4299390900","https://openalex.org/W6600182994","https://openalex.org/W6611371219"],"related_works":["https://openalex.org/W288388583","https://openalex.org/W1995120876","https://openalex.org/W2350176099","https://openalex.org/W2491940682","https://openalex.org/W2796622564","https://openalex.org/W2076278624","https://openalex.org/W2980408391","https://openalex.org/W423103167","https://openalex.org/W207680367","https://openalex.org/W1504849543"],"abstract_inverted_index":{"In":[0,67],"this":[1],"paper":[2],"we":[3,39],"are":[4,46,62],"concerned":[5],"with":[6],"soft":[7],"applications":[8],"of":[9,12,53,75,84],"the":[10,51,76,82],"axiom":[11,83],"choice":[13],"{AC)":[14],"in":[15,24,64,70,89],"general":[16],"topology.":[17],"We":[18],"define":[19],"16":[20],"properties":[21],"which":[22],"hold":[23],"ZF":[25],"for":[26],"each":[27],"T":[28],"2":[29],"space,":[30],"if":[31,34],"and":[32,38],"only":[33],"AC":[35,49,54],"is":[36,56,87],"true,":[37],"investigate":[40],"what":[41],"implications":[42,78],"between":[43],"these":[44],"axioms":[45],"provable":[47],"without":[48],"(in":[50],"presence":[52],"there":[55],"nothing":[57],"to":[58,79],"prove).":[59],"Our":[60],"results":[61],"summarized":[63],"two":[65],"diagrams.":[66],"Figure":[68,90],"Counterexamples":[69],"three":[71],"models":[72],"prove":[73],"188":[74],"possible":[77],"depend":[80],"on":[81],"choice,":[85],"as":[86],"shown":[88]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}