{"id":"https://openalex.org/W3019804224","doi":"https://doi.org/10.1142/s0219061322500143","title":"Complexity of distances: Theory of generalized analytic equivalence relations","display_name":"Complexity of distances: Theory of generalized analytic equivalence relations","publication_year":2022,"publication_date":"2022-06-17","ids":{"openalex":"https://openalex.org/W3019804224","doi":"https://doi.org/10.1142/s0219061322500143","mag":"3019804224"},"language":"en","primary_location":{"id":"doi:10.1142/s0219061322500143","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219061322500143","pdf_url":null,"source":{"id":"https://openalex.org/S29890666","display_name":"Journal of Mathematical Logic","issn_l":"0219-0613","issn":["0219-0613","1793-6691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Logic","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1804.11164","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5065460820","display_name":"Marek C\u00fath","orcid":"https://orcid.org/0000-0001-6688-8004"},"institutions":[{"id":"https://openalex.org/I21250087","display_name":"Charles University","ror":"https://ror.org/024d6js02","country_code":"CZ","type":"education","lineage":["https://openalex.org/I21250087"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Marek C\u00fath","raw_affiliation_strings":["Charles University, Faculty of Mathematics and Physics, Department of Mathematical, Analysis, Sokolovsk\u00e1 83, 186 75 Prague 8, Czech Republic"],"affiliations":[{"raw_affiliation_string":"Charles University, Faculty of Mathematics and Physics, Department of Mathematical, Analysis, Sokolovsk\u00e1 83, 186 75 Prague 8, Czech Republic","institution_ids":["https://openalex.org/I21250087"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018422403","display_name":"Michal Doucha","orcid":"https://orcid.org/0000-0003-3675-1378"},"institutions":[{"id":"https://openalex.org/I4210120266","display_name":"Czech Academy of Sciences, Institute of Mathematics","ror":"https://ror.org/02tv1yf50","country_code":"CZ","type":"facility","lineage":["https://openalex.org/I202391551","https://openalex.org/I4210120266"]}],"countries":["CZ"],"is_corresponding":true,"raw_author_name":"Michal Doucha","raw_affiliation_strings":["Institute of Mathematics of the Czech Academy of Sciences, \u017ditn\u00e1 25, 115 67 Prague 1, Czech Republic"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics of the Czech Academy of Sciences, \u017ditn\u00e1 25, 115 67 Prague 1, Czech Republic","institution_ids":["https://openalex.org/I4210120266"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087468417","display_name":"Ond\u0159ej Kurka","orcid":"https://orcid.org/0000-0001-8560-437X"},"institutions":[{"id":"https://openalex.org/I4210120266","display_name":"Czech Academy of Sciences, Institute of Mathematics","ror":"https://ror.org/02tv1yf50","country_code":"CZ","type":"facility","lineage":["https://openalex.org/I202391551","https://openalex.org/I4210120266"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Ond\u0159ej Kurka","raw_affiliation_strings":["Institute of Mathematics of the Czech Academy of Sciences, \u017ditn\u00e1 25, 115 67 Prague 1, Czech Republic"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics of the Czech Academy of Sciences, \u017ditn\u00e1 25, 115 67 Prague 1, Czech Republic","institution_ids":["https://openalex.org/I4210120266"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5018422403"],"corresponding_institution_ids":["https://openalex.org/I4210120266"],"apc_list":null,"apc_paid":null,"fwci":1.9982,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.84093484,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"23","issue":"01","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9995999932289124,"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":0.9995999932289124,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9951000213623047,"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":0.9830999970436096,"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/mathematics","display_name":"Mathematics","score":0.9142082929611206},{"id":"https://openalex.org/keywords/borel-equivalence-relation","display_name":"Borel equivalence relation","score":0.6620856523513794},{"id":"https://openalex.org/keywords/equivalence-relation","display_name":"Equivalence relation","score":0.6612611413002014},{"id":"https://openalex.org/keywords/borel-set","display_name":"Borel set","score":0.6420189738273621},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5992195010185242},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.5590615272521973},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.47506922483444214},{"id":"https://openalex.org/keywords/hausdorff-space","display_name":"Hausdorff space","score":0.4552830457687378},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44649943709373474},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.41755929589271545},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4132333993911743},{"id":"https://openalex.org/keywords/borel-measure","display_name":"Borel measure","score":0.39728492498397827},{"id":"https://openalex.org/keywords/probability-measure","display_name":"Probability measure","score":0.19077923893928528},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14271950721740723}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9142082929611206},{"id":"https://openalex.org/C5278979","wikidata":"https://www.wikidata.org/wiki/Q4944905","display_name":"Borel equivalence relation","level":4,"score":0.6620856523513794},{"id":"https://openalex.org/C156103551","wikidata":"https://www.wikidata.org/wiki/Q130998","display_name":"Equivalence relation","level":2,"score":0.6612611413002014},{"id":"https://openalex.org/C39952206","wikidata":"https://www.wikidata.org/wiki/Q21086747","display_name":"Borel set","level":2,"score":0.6420189738273621},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5992195010185242},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5590615272521973},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.47506922483444214},{"id":"https://openalex.org/C191399826","wikidata":"https://www.wikidata.org/wiki/Q326908","display_name":"Hausdorff space","level":2,"score":0.4552830457687378},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44649943709373474},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.41755929589271545},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4132333993911743},{"id":"https://openalex.org/C166758865","wikidata":"https://www.wikidata.org/wiki/Q892585","display_name":"Borel measure","level":3,"score":0.39728492498397827},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.19077923893928528},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14271950721740723},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0219061322500143","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219061322500143","pdf_url":null,"source":{"id":"https://openalex.org/S29890666","display_name":"Journal of Mathematical Logic","issn_l":"0219-0613","issn":["0219-0613","1793-6691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Logic","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1804.11164","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1804.11164","pdf_url":"https://arxiv.org/pdf/1804.11164","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1804.11164","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1804.11164","pdf_url":"https://arxiv.org/pdf/1804.11164","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":null,"raw_type":"text"},"sustainable_development_goals":[{"score":0.4099999964237213,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":55,"referenced_works":["https://openalex.org/W121267321","https://openalex.org/W273178449","https://openalex.org/W633446433","https://openalex.org/W635392658","https://openalex.org/W1483415350","https://openalex.org/W1483679902","https://openalex.org/W1517743699","https://openalex.org/W1523918473","https://openalex.org/W1533233993","https://openalex.org/W1539382740","https://openalex.org/W1542113445","https://openalex.org/W1590951015","https://openalex.org/W1602868010","https://openalex.org/W1637852107","https://openalex.org/W1671098680","https://openalex.org/W1860088429","https://openalex.org/W1879277083","https://openalex.org/W1909320773","https://openalex.org/W1912497050","https://openalex.org/W1967901127","https://openalex.org/W1975162150","https://openalex.org/W1988683400","https://openalex.org/W1996053791","https://openalex.org/W1997553844","https://openalex.org/W2005622099","https://openalex.org/W2014124152","https://openalex.org/W2019049310","https://openalex.org/W2022813695","https://openalex.org/W2027973842","https://openalex.org/W2031149828","https://openalex.org/W2032916024","https://openalex.org/W2033367123","https://openalex.org/W2079592820","https://openalex.org/W2089793319","https://openalex.org/W2111754130","https://openalex.org/W2131682197","https://openalex.org/W2140891656","https://openalex.org/W2145406042","https://openalex.org/W2149667568","https://openalex.org/W2152586010","https://openalex.org/W2157239786","https://openalex.org/W2264455805","https://openalex.org/W2322033177","https://openalex.org/W2333307005","https://openalex.org/W2498059247","https://openalex.org/W2570044735","https://openalex.org/W2964213221","https://openalex.org/W3020086861","https://openalex.org/W3098189590","https://openalex.org/W3100602695","https://openalex.org/W4213358110","https://openalex.org/W4252290972","https://openalex.org/W4298377646","https://openalex.org/W4403473074","https://openalex.org/W6820385466"],"related_works":["https://openalex.org/W2122677906","https://openalex.org/W1491956444","https://openalex.org/W110058238","https://openalex.org/W2031042539","https://openalex.org/W2140891656","https://openalex.org/W1575382216","https://openalex.org/W2114381574","https://openalex.org/W1541348852","https://openalex.org/W2046711029","https://openalex.org/W2783157730"],"abstract_inverted_index":{"We":[0,31,44,109],"generalize":[1],"the":[2,46,54,58,66,102,126,143,152,167,172],"notion":[3,48],"of":[4,49,68,105,115,154,166],"analytic/Borel":[5,22],"equivalence":[6,9],"relations,":[7,10],"orbit":[8,24,99],"and":[11,19,26,37,79,83,107,120,128,159,179],"Borel":[12,27],"reductions":[13,28,170],"between":[14,29,171],"them":[15],"to":[16,95],"their":[17],"continuous":[18],"quantitative":[20],"counterparts:":[21],"pseudometrics,":[23,25,100],"them.":[30],"motivate":[32],"these":[33],"concepts":[34],"on":[35,65,122],"examples":[36],"we":[38,86,135],"set":[39],"some":[40],"basic":[41],"general":[42],"theory.":[43],"illustrate":[45],"new":[47,137],"reduction":[50],"by":[51,98],"showing":[52,141],"that":[53,88,142],"Gromov\u2013Hausdorff":[55,127],"distance":[56],"maintains":[57],"same":[59],"complexity":[60],"if":[61],"it":[62],"is":[63,92,162],"defined":[64],"class":[67],"all":[69],"Polish":[70],"metric":[71,180],"spaces,":[72],"spaces":[73],"bounded":[74],"from":[75,77,80,176],"below,":[76],"above,":[78],"both":[81],"below":[82],"above.":[84],"Then":[85],"show":[87],"[Formula:":[89],"see":[90],"text]":[91],"not":[93],"reducible":[94],"equivalences":[96],"induced":[97],"generalizing":[101],"seminal":[103],"result":[104],"Kechris":[106],"Louveau.":[108],"answer":[110],"in":[111,125,146],"negative":[112],"a":[113,163],"question":[114],"Ben":[116,155],"Yaacov,":[117,156],"Doucha,":[118,157],"Nies,":[119,158],"Tsankov":[121],"whether":[123],"balls":[124],"Kadets":[129],"distances":[130],"are":[131,149,182],"Borel.":[132],"In":[133],"appendix,":[134],"provide":[136],"methods":[138],"using":[139],"games":[140],"distance-zero":[144],"classes":[145],"certain":[147],"pseudometrics":[148,175],"Borel,":[150],"extending":[151],"results":[153],"Tsankov.":[160],"There":[161],"complementary":[164],"paper":[165],"authors":[168],"where":[169],"most":[173],"common":[174],"functional":[177],"analysis":[178],"geometry":[181],"provided.":[183]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2019,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
