{"id":"https://openalex.org/W2034766707","doi":"https://doi.org/10.1002/malq.201020039","title":"Compact and Loeb Hausdorff spaces in \\documentclass{article}\\usepackage{amssymb}\\begin{document}\\pagestyle{empty}$\\mathsf {ZF}$\\end{document} and the axiom of choice for families of finite sets","display_name":"Compact and Loeb Hausdorff spaces in \\documentclass{article}\\usepackage{amssymb}\\begin{document}\\pagestyle{empty}$\\mathsf {ZF}$\\end{document} and the axiom of choice for families of finite sets","publication_year":2012,"publication_date":"2012-04-25","ids":{"openalex":"https://openalex.org/W2034766707","doi":"https://doi.org/10.1002/malq.201020039","mag":"2034766707"},"language":"en","primary_location":{"id":"doi:10.1002/malq.201020039","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.201020039","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":"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/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":0.8192,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.70132172,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"58","issue":"3","first_page":"130","last_page":"138"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9998000264167786,"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":0.9998000264167786,"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9914000034332275,"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/T11545","display_name":"Advanced Banach Space Theory","score":0.9815000295639038,"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/physics","display_name":"Physics","score":0.6310440301895142},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5977801084518433},{"id":"https://openalex.org/keywords/backslash","display_name":"Backslash","score":0.5150792002677917},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.4416431486606598},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.32271796464920044},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.11283844709396362}],"concepts":[{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.6310440301895142},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5977801084518433},{"id":"https://openalex.org/C2780345915","wikidata":"https://www.wikidata.org/wiki/Q11185","display_name":"Backslash","level":2,"score":0.5150792002677917},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.4416431486606598},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.32271796464920044},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.11283844709396362}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/malq.201020039","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.201020039","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":"Mathematical Logic Quarterly","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W949064508","https://openalex.org/W1608084331","https://openalex.org/W1967842301","https://openalex.org/W1978911266","https://openalex.org/W1980590548","https://openalex.org/W1998126380","https://openalex.org/W2065892031","https://openalex.org/W2088257207","https://openalex.org/W2169230382","https://openalex.org/W2323053796","https://openalex.org/W4239720385"],"related_works":["https://openalex.org/W2935759653","https://openalex.org/W3105167352","https://openalex.org/W54078636","https://openalex.org/W2954470139","https://openalex.org/W1501425562","https://openalex.org/W2902782467","https://openalex.org/W3084825885","https://openalex.org/W2298861036","https://openalex.org/W3148032049","https://openalex.org/W2399831189"],"abstract_inverted_index":{"Abstract":[0],"Given":[1],"a":[2,18,45,81,104,137,155,216,236],"set":[3,20,83,106,125,203,218,224,238],"X":[4,49,126,204,225],",":[5,127,205,226],"\\documentclass{article}\\usepackage{amssymb}\\begin{document}\\pagestyle{empty}$\\mathsf":[6,58,60,63,66,87,90,108,111,114,140,181,186,191],"{AC}^{\\mathrm{fin}(X)}$\\end{document}":[7,88,187],"denotes":[8,28],"the":[9,29,36,53,56,162,169],"statement:":[10],"\u201c":[11,71,145,200,206,221,241],"\\documentclass{article}\\usepackage{amssymb}\\begin{document}\\pagestyle{empty}$[X]^{<\\omega":[12],"}\\backslash":[13],"\\lbrace":[14,77,100,133,151,177,212,232,254],"\\varnothing":[15,78,101,134,152,178,213,233,255],"\\rbrace$\\end{document}":[16,79,102,135,153,179,214,234],"has":[17,80,103,136,154,215,235],"choice":[19,82,105,138,156,217,237],"\u201d":[21,219,239],"and":[22,70],"\\documentclass{article}\\usepackage{amssymb}\\begin{document}\\pagestyle{empty}$\\mathcal":[23,72,95,128,146,158,174,207,227,251],"{C}_\\mathrm{R}\\big":[24,73,96,129],"(\\mathbf":[25,74,97,130,148,209,229],"{2}^{X}\\big":[26,75,98,131,149,210],")$\\end{document}":[27],"family":[30,163],"of":[31,35,48,119,164,168,247],"all":[32,165],"closed":[33,166],"subsets":[34,167],"topological":[37],"space":[38,170],"\\documentclass{article}\\usepackage{amssymb}\\begin{document}\\pagestyle{empty}$\\mathbf":[39,171,245],"{2}^{X}$\\end{document}":[40],"whose":[41],"definition":[42],"depends":[43],"on":[44],"finite":[46,120,248],"subset":[47],".":[50,110,195],"We":[51,85,196],"study":[52],"interrelations":[54],"between":[55],"statements":[57],"{AC}^{\\mathrm{fin}(X)},$\\end{document}":[59],"{AC}^{\\mathrm{fin}([X]^{<\\omega":[61,91],"})},$\\end{document}":[62],"{AC}^{\\mathrm{fin}":[64],"(F_{n}(X,2))},$\\end{document}":[65],"{AC}^{\\mathrm{fin}(\\mathcal":[67,182,192],"{\\wp":[68,183,193],"}(X))}$\\end{document}":[69,184,194],")\\backslash":[76,99,132,150,211,231],"\u201d.":[84],"show:":[86],"iff":[89,94,107,122,220,240],"}":[92],")}$\\end{document}":[93],"{AC}^{\\mathrm{fin}(F_{n}(X,2))}$\\end{document}":[109],"{AC}_{\\mathrm{fin}}$\\end{document}":[112,141],"(":[113],"{AC}$\\end{document}":[115],"restricted":[116],"to":[117],"families":[118],"sets)":[121],"for":[123,222,242],"every":[124,202,223,243],"set.":[139],"does":[142,188],"not":[143,189],"imply":[144,190],"{K}\\big":[147,208,228],"set(":[157],"{K}(\\mathbf":[159,175,252],"{X})$\\end{document}":[160],"is":[161],"{X}$\\end{document}":[172,246],")":[173],"{2}^{X})\\backslash":[176],"implies":[180],"but":[185],"also":[197],"show":[198],"that":[199],"For":[201],"{[0,1]}^{X}\\big":[230],"product":[244],"discrete":[249],"spaces,":[250],"{X})\\backslash":[253],"\\rbrace$\\end{":[256]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}