{"id":"https://openalex.org/W202171158","doi":"https://doi.org/10.1002/1521-3870(200010)46:4<569::aid-malq569>3.0.co;2-j","title":"The Compactness of 2 and the Axiom of Choice","display_name":"The Compactness of 2 and the Axiom of Choice","publication_year":2000,"publication_date":"2000-10-01","ids":{"openalex":"https://openalex.org/W202171158","doi":"https://doi.org/10.1002/1521-3870(200010)46:4<569::aid-malq569>3.0.co;2-j","mag":"202171158"},"language":"en","primary_location":{"id":"doi:10.1002/1521-3870(200010)46:4<569::aid-malq569>3.0.co;2-j","is_oa":false,"landing_page_url":"https://doi.org/10.1002/1521-3870(200010)46:4<569::aid-malq569>3.0.co;2-j","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0044-3050","issn":["0044-3050","0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"MLQ","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/A5028285276","display_name":"Kyriakos Keremedis","orcid":"https://orcid.org/0000-0001-8453-3477"},"institutions":[{"id":"https://openalex.org/I98805295","display_name":"University of the Aegean","ror":"https://ror.org/03zsp3p94","country_code":"GR","type":"education","lineage":["https://openalex.org/I98805295"]}],"countries":["GR"],"is_corresponding":true,"raw_author_name":"Kyriakos Keremedis","raw_affiliation_strings":["Department of Mathematics, University of the Aegean, Karlovasi, 83200 Samos, Greece","Department of Mathematics, University of the Aegean, Karlovasi, 83200, SAmos, Greece"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of the Aegean, Karlovasi, 83200 Samos, Greece","institution_ids":["https://openalex.org/I98805295"]},{"raw_affiliation_string":"Department of Mathematics, University of the Aegean, Karlovasi, 83200, SAmos, Greece","institution_ids":["https://openalex.org/I98805295"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5028285276"],"corresponding_institution_ids":["https://openalex.org/I98805295"],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.02327824,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"46","issue":"4","first_page":"569","last_page":"571"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9984999895095825,"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":0.9984999895095825,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9821000099182129,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9355999827384949,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"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":0.9111737012863159},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8483597636222839},{"id":"https://openalex.org/keywords/compact-space","display_name":"Compact space","score":0.8073146939277649},{"id":"https://openalex.org/keywords/tychonoff-space","display_name":"Tychonoff space","score":0.6204844117164612},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.5225757360458374},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.45817089080810547},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.41187530755996704},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.38088488578796387},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37470197677612305},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3243587017059326},{"id":"https://openalex.org/keywords/hausdorff-space","display_name":"Hausdorff space","score":0.2688167691230774},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.1730918288230896},{"id":"https://openalex.org/keywords/set-theory","display_name":"Set theory","score":0.14460453391075134},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0818357765674591},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06010943651199341}],"concepts":[{"id":"https://openalex.org/C151797676","wikidata":"https://www.wikidata.org/wiki/Q179692","display_name":"Axiom of choice","level":4,"score":0.9111737012863159},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8483597636222839},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.8073146939277649},{"id":"https://openalex.org/C87142424","wikidata":"https://www.wikidata.org/wiki/Q1191433","display_name":"Tychonoff space","level":3,"score":0.6204844117164612},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.5225757360458374},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.45817089080810547},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.41187530755996704},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.38088488578796387},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37470197677612305},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3243587017059326},{"id":"https://openalex.org/C191399826","wikidata":"https://www.wikidata.org/wiki/Q326908","display_name":"Hausdorff space","level":2,"score":0.2688167691230774},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.1730918288230896},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.14460453391075134},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0818357765674591},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06010943651199341},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/1521-3870(200010)46:4<569::aid-malq569>3.0.co;2-j","is_oa":false,"landing_page_url":"https://doi.org/10.1002/1521-3870(200010)46:4<569::aid-malq569>3.0.co;2-j","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0044-3050","issn":["0044-3050","0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"MLQ","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3112295066","https://openalex.org/W3124617235","https://openalex.org/W2065652849","https://openalex.org/W4235989149","https://openalex.org/W4210343663","https://openalex.org/W2373903136","https://openalex.org/W2088257207","https://openalex.org/W2384118119","https://openalex.org/W4386999744","https://openalex.org/W154021799"],"abstract_inverted_index":{"We":[0],"show":[1],"that":[2],"for":[3],"every":[4],"we":[5],"ordered":[6],"cardinal":[7],"number":[8],"m":[9],"the":[10,19],"Tychonoff":[11],"product":[12],"2m":[13],"is":[14,30],"a":[15],"compact":[16],"space":[17],"without":[18],"use":[20],"of":[21],"any":[22],"choice":[23],"but":[24],"in":[25],"Cohen's":[26],"Second":[27],"Mode":[28],"2\u211d":[29],"not":[31],"compact.":[32]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
