{"id":"https://openalex.org/W4235989149","doi":"https://doi.org/10.1002/malq.200310004","title":"Products of compact spaces and the axiom of choice II","display_name":"Products of compact spaces and the axiom of choice II","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W4235989149","doi":"https://doi.org/10.1002/malq.200310004"},"language":"en","primary_location":{"id":"doi:10.1002/malq.200310004","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.200310004","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0942-5616","issn":["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":"Mathematical Logic Quarterly","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":["Department of Mathematics, Purdue University, West Lafayette, IN 47907, U.S.A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Purdue University, West Lafayette, IN 47907, U.S.A","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":["Department of Mathematics, Purdue University, West Lafayette, IN 47907, U.S.A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Purdue University, West Lafayette, IN 47907, U.S.A","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":["Department of Mathematics, Eastern Michigan University, Ypsilanti, MI 48197, U, S.A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Eastern Michigan University, Ypsilanti, MI 48197, U, S.A","institution_ids":["https://openalex.org/I138216421"]}]},{"author_position":"middle","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":false,"raw_author_name":"Kyriakos Keremedis","raw_affiliation_strings":["Department of Mathematics, University of the Aegean, Karlovasi, Samos, 83200, Greece"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of the Aegean, Karlovasi, Samos, 83200, Greece","institution_ids":["https://openalex.org/I98805295"]}]},{"author_position":"last","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"]},{"id":"https://openalex.org/I4210165376","display_name":"October 6 University","ror":"https://ror.org/05y06tg49","country_code":"EG","type":"education","lineage":["https://openalex.org/I4210165376"]}],"countries":["EG","US"],"is_corresponding":false,"raw_author_name":"Jean E. Rubin","raw_affiliation_strings":["Department of Mathematics, Purdue University, West Lafayette, IN 47907, U.S.A","Jean Rubin died on October 25, 2002"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Purdue University, West Lafayette, IN 47907, U.S.A","institution_ids":["https://openalex.org/I219193219"]},{"raw_affiliation_string":"Jean Rubin died on October 25, 2002","institution_ids":["https://openalex.org/I4210165376"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":null,"fwci":1.7395,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.85010606,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"49","issue":"1","first_page":"57","last_page":"71"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9987999796867371,"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":0.9987999796867371,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.9843999743461609,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9679999947547913,"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/mathematics","display_name":"Mathematics","score":0.8781067132949829},{"id":"https://openalex.org/keywords/tychonoff-space","display_name":"Tychonoff space","score":0.8726891279220581},{"id":"https://openalex.org/keywords/axiom-of-choice","display_name":"Axiom of choice","score":0.8127402067184448},{"id":"https://openalex.org/keywords/hausdorff-space","display_name":"Hausdorff space","score":0.6902708411216736},{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.6870508193969727},{"id":"https://openalex.org/keywords/compact-space","display_name":"Compact space","score":0.6661882400512695},{"id":"https://openalex.org/keywords/separation-axiom","display_name":"Separation axiom","score":0.6199482083320618},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.5730732679367065},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.5401498079299927},{"id":"https://openalex.org/keywords/continuation","display_name":"Continuation","score":0.5138111710548401},{"id":"https://openalex.org/keywords/axiom-independence","display_name":"Axiom independence","score":0.4904048442840576},{"id":"https://openalex.org/keywords/urysohn-and-completely-hausdorff-spaces","display_name":"Urysohn and completely Hausdorff spaces","score":0.4875866770744324},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4160369634628296},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40624141693115234},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.20398330688476562},{"id":"https://openalex.org/keywords/set-theory","display_name":"Set theory","score":0.1865478754043579},{"id":"https://openalex.org/keywords/hausdorff-measure","display_name":"Hausdorff measure","score":0.10900899767875671},{"id":"https://openalex.org/keywords/hausdorff-dimension","display_name":"Hausdorff dimension","score":0.08149710297584534},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.05426248908042908}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8781067132949829},{"id":"https://openalex.org/C87142424","wikidata":"https://www.wikidata.org/wiki/Q1191433","display_name":"Tychonoff space","level":3,"score":0.8726891279220581},{"id":"https://openalex.org/C151797676","wikidata":"https://www.wikidata.org/wiki/Q179692","display_name":"Axiom of choice","level":4,"score":0.8127402067184448},{"id":"https://openalex.org/C191399826","wikidata":"https://www.wikidata.org/wiki/Q326908","display_name":"Hausdorff space","level":2,"score":0.6902708411216736},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.6870508193969727},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.6661882400512695},{"id":"https://openalex.org/C40409056","wikidata":"https://www.wikidata.org/wiki/Q1140985","display_name":"Separation axiom","level":3,"score":0.6199482083320618},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.5730732679367065},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.5401498079299927},{"id":"https://openalex.org/C88626702","wikidata":"https://www.wikidata.org/wiki/Q1128903","display_name":"Continuation","level":2,"score":0.5138111710548401},{"id":"https://openalex.org/C170088968","wikidata":"https://www.wikidata.org/wiki/Q4830547","display_name":"Axiom independence","level":3,"score":0.4904048442840576},{"id":"https://openalex.org/C84496893","wikidata":"https://www.wikidata.org/wiki/Q1135782","display_name":"Urysohn and completely Hausdorff spaces","level":4,"score":0.4875866770744324},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4160369634628296},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40624141693115234},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.20398330688476562},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.1865478754043579},{"id":"https://openalex.org/C73225184","wikidata":"https://www.wikidata.org/wiki/Q1591095","display_name":"Hausdorff measure","level":3,"score":0.10900899767875671},{"id":"https://openalex.org/C194198291","wikidata":"https://www.wikidata.org/wiki/Q565186","display_name":"Hausdorff dimension","level":2,"score":0.08149710297584534},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.05426248908042908},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1002/malq.200310004","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.200310004","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0942-5616","issn":["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":"Mathematical Logic Quarterly","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.87.5844","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.87.5844","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/pro2-12.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W245573756","https://openalex.org/W328650061","https://openalex.org/W949064508","https://openalex.org/W955266649","https://openalex.org/W1990682234","https://openalex.org/W1995975622","https://openalex.org/W2014317630","https://openalex.org/W2020053991","https://openalex.org/W2334527086","https://openalex.org/W4230977178","https://openalex.org/W4233444413","https://openalex.org/W4255340608"],"related_works":["https://openalex.org/W2389902974","https://openalex.org/W1995120876","https://openalex.org/W2484407303","https://openalex.org/W288388583","https://openalex.org/W1504849543","https://openalex.org/W2017671599","https://openalex.org/W4235989149","https://openalex.org/W2147242351","https://openalex.org/W2390945607","https://openalex.org/W4285273086"],"abstract_inverted_index":{"Abstract":[0],"This":[1],"is":[2],"a":[3],"continuation":[4],"of":[5,16,22,33],"[2].":[6],"We":[7,37],"study":[8,39],"the":[9,45,48],"Tychonoff":[10,42],"Compactness":[11],"Theorem":[12],"for":[13,19],"various":[14,20],"definitions":[15],"compactness":[17],"and":[18,25,31,44],"types":[21],"spaces":[23],"(first":[24],"second":[26],"countable":[27],"spaces,":[28,30],"Hausdorff":[29],"subspaces":[32],"\u211d":[34],"K":[35],").":[36],"also":[38],"well":[40],"ordered":[41],"products":[43],"effect":[46],"that":[47],"multiple":[49],"choice":[50],"axiom":[51],"has":[52],"on":[53],"such":[54],"products.":[55]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}