{"id":"https://openalex.org/W2097624663","doi":"https://doi.org/10.2307/2695084","title":"Actions of non-compact and non-locally compact Polish groups","display_name":"Actions of non-compact and non-locally compact Polish groups","publication_year":2000,"publication_date":"2000-12-01","ids":{"openalex":"https://openalex.org/W2097624663","doi":"https://doi.org/10.2307/2695084","mag":"2097624663"},"language":"en","primary_location":{"id":"doi:10.2307/2695084","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2695084","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","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/A5012953076","display_name":"S\u0142awomir Solecki","orcid":"https://orcid.org/0000-0003-4152-1585"},"institutions":[{"id":"https://openalex.org/I4210119109","display_name":"Indiana University Bloomington","ror":"https://ror.org/02k40bc56","country_code":"US","type":"education","lineage":["https://openalex.org/I4210119109","https://openalex.org/I592451"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"S\u0142awomir Solecki","raw_affiliation_strings":["Department of Mathematics, Indiana University, Bloomington, IN 47405, USA, E-mail:","Department of Mathematics, Indiana University, Bloomington, IN 47405, USA, E-mail: ssolecki@indiana.edu"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Indiana University, Bloomington, IN 47405, USA, E-mail:","institution_ids":["https://openalex.org/I4210119109"]},{"raw_affiliation_string":"Department of Mathematics, Indiana University, Bloomington, IN 47405, USA, E-mail: ssolecki@indiana.edu","institution_ids":["https://openalex.org/I4210119109"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5012953076"],"corresponding_institution_ids":["https://openalex.org/I4210119109"],"apc_list":null,"apc_paid":null,"fwci":1.0038,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.74870112,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"65","issue":"4","first_page":"1881","last_page":"1894"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9977999925613403,"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":0.9977999925613403,"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/mathematics","display_name":"Mathematics","score":0.8348912000656128},{"id":"https://openalex.org/keywords/borel-equivalence-relation","display_name":"Borel equivalence relation","score":0.792664647102356},{"id":"https://openalex.org/keywords/polish-space","display_name":"Polish space","score":0.7755601406097412},{"id":"https://openalex.org/keywords/equivalence-relation","display_name":"Equivalence relation","score":0.7508511543273926},{"id":"https://openalex.org/keywords/compact-space","display_name":"Compact space","score":0.7331834435462952},{"id":"https://openalex.org/keywords/separable-space","display_name":"Separable space","score":0.7073138952255249},{"id":"https://openalex.org/keywords/locally-compact-space","display_name":"Locally compact space","score":0.6354824900627136},{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.5942512154579163},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.5888902544975281},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5842245817184448},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.5672007203102112},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.5203285217285156},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4728907644748688},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.4571925699710846},{"id":"https://openalex.org/keywords/orbit","display_name":"Orbit (dynamics)","score":0.43560537695884705},{"id":"https://openalex.org/keywords/action","display_name":"Action (physics)","score":0.42454037070274353},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2963465452194214},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2693547010421753},{"id":"https://openalex.org/keywords/borel-measure","display_name":"Borel measure","score":0.20161694288253784},{"id":"https://openalex.org/keywords/probability-measure","display_name":"Probability measure","score":0.0778786838054657},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06877568364143372}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8348912000656128},{"id":"https://openalex.org/C5278979","wikidata":"https://www.wikidata.org/wiki/Q4944905","display_name":"Borel equivalence relation","level":4,"score":0.792664647102356},{"id":"https://openalex.org/C31316033","wikidata":"https://www.wikidata.org/wiki/Q1207972","display_name":"Polish space","level":3,"score":0.7755601406097412},{"id":"https://openalex.org/C156103551","wikidata":"https://www.wikidata.org/wiki/Q130998","display_name":"Equivalence relation","level":2,"score":0.7508511543273926},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.7331834435462952},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.7073138952255249},{"id":"https://openalex.org/C31498916","wikidata":"https://www.wikidata.org/wiki/Q583034","display_name":"Locally compact space","level":2,"score":0.6354824900627136},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.5942512154579163},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.5888902544975281},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5842245817184448},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5672007203102112},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.5203285217285156},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4728907644748688},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4571925699710846},{"id":"https://openalex.org/C196644772","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Orbit (dynamics)","level":2,"score":0.43560537695884705},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.42454037070274353},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2963465452194214},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2693547010421753},{"id":"https://openalex.org/C166758865","wikidata":"https://www.wikidata.org/wiki/Q892585","display_name":"Borel measure","level":3,"score":0.20161694288253784},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.0778786838054657},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06877568364143372},{"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/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2695084","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2695084","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1183746272","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183746272","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":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W1531605312","https://openalex.org/W1539382740","https://openalex.org/W1602868010","https://openalex.org/W1969761980","https://openalex.org/W2024078235","https://openalex.org/W2067916929","https://openalex.org/W2152501852"],"related_works":["https://openalex.org/W1972195264","https://openalex.org/W4302132510","https://openalex.org/W2963349776","https://openalex.org/W2264355049","https://openalex.org/W2114381574","https://openalex.org/W2122677906","https://openalex.org/W2139131833","https://openalex.org/W110058238","https://openalex.org/W3161578274","https://openalex.org/W2173118844"],"abstract_inverted_index":{"Abstract":[0],"We":[1,21,52],"show":[2],"that":[3,84,88,110],"each":[4,85],"non-compact":[5],"Polish":[6,14,31,101],"group":[7,32,43,61],"admits":[8],"a":[9,13,24,30,48,78,96,100],"continuous":[10,38,97],"action":[11,98],"on":[12,99],"space":[15,94,102],"with":[16,62,103],"non-smooth":[17],"orbit":[18,67,105],"equivalence":[19,68,75,106],"relation.":[20],"actually":[22],"construct":[23],"free":[25,39],"such":[26],"action.":[27],"Thus":[28],"for":[29],"compactness":[33,58,115],"is":[34],"equivalent":[35],"to":[36,65,72],"all":[37],"actions":[40],"of":[41,50,59,80],"this":[42,111],"being":[44],"smooth.":[45],"This":[46],"answers":[47],"question":[49],"Kechris.":[51],"also":[53],"establish":[54],"results":[55],"relating":[56],"local":[57],"the":[60],"its":[63],"inability":[64],"induce":[66],"relations":[69],"not":[70],"reducible":[71],"countable":[73],"Borel":[74],"relations.":[76],"Generalizing":[77],"result":[79],"Hjorth,":[81],"we":[82],"prove":[83],"non-locally":[86],"compact,":[87],"is,":[89],"infinite":[90],"dimensional,":[91],"separable":[92],"Banach":[93,117],"has":[95],"non-Borel":[104],"relation,":[107],"thus":[108],"showing":[109],"property":[112],"characterizes":[113],"non-local":[114],"among":[116],"spaces.":[118]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2015,"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"}
