{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,23]],"date-time":"2023-10-23T11:24:42Z","timestamp":1698060282622},"reference-count":9,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":4849,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2000,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We show that each non-compact Polish group admits a continuous action on a Polish space with non-smooth orbit equivalence relation. We actually construct a free such action. Thus for a Polish group compactness is equivalent to all continuous free actions of this group being smooth. This answers a question of Kechris. We also establish results relating local compactness of the group with its inability to induce orbit equivalence relations not reducible to countable Borel equivalence relations. Generalizing a result of Hjorth, we prove that each non-locally compact, that is, infinite dimensional, separable Banach space has a continuous action on a Polish space with non-Borel orbit equivalence relation, thus showing that this property characterizes non-local compactness among Banach spaces.<\/jats:p>","DOI":"10.2307\/2695084","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T18:05:00Z","timestamp":1146938700000},"page":"1881-1894","source":"Crossref","is-referenced-by-count":7,"title":["Actions of non-compact and non-locally compact Polish groups"],"prefix":"10.1017","volume":"65","author":[{"given":"S\u0142awomir","family":"Solecki","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200011695_ref009","doi-asserted-by":"publisher","DOI":"10.1016\/S0166-8641(96)00119-8"},{"key":"S0022481200011695_ref008","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1995-1311918-2"},{"key":"S0022481200011695_ref007","unstructured":"Kechris A. S. , Lectures on definable group actions and equivalence relations, lecture notes."},{"key":"S0022481200011695_ref006","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4190-4"},{"key":"S0022481200011695_ref002","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-5200-9"},{"key":"S0022481200011695_ref001","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511735264"},{"key":"S0022481200011695_ref005","doi-asserted-by":"publisher","DOI":"10.1017\/S0143385700006751"},{"key":"S0022481200011695_ref004","unstructured":"Hjorth G. , Actions by the classical Banach spaces, this Journal, to appear."},{"key":"S0022481200011695_ref003","doi-asserted-by":"publisher","DOI":"10.1016\/0001-8708(85)90091-X"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200011695","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,8]],"date-time":"2019-05-08T19:57:50Z","timestamp":1557345470000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200011695\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,12]]},"references-count":9,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2000,12]]}},"alternative-id":["S0022481200011695"],"URL":"https:\/\/doi.org\/10.2307\/2695084","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,12]]}}}