Dichotomy for arithmetic progressions in subsets of reals

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dc.citation.firstpage5029en_US
dc.citation.journalTitleProceedings of the American Mathematical Societyen_US
dc.citation.lastpage5034en_US
dc.citation.volumeNumber144en_US
dc.contributor.authorBoshernitzan, Michaelen_US
dc.contributor.authorChaika, Jonen_US
dc.date.accessioned2017-05-22T21:48:43Zen_US
dc.date.available2017-05-22T21:48:43Zen_US
dc.date.issued2016en_US
dc.description.abstractLet H stand for the set of homeomorphisms φ:[0, 1] → [0, 1]. We prove the following dichotomy for Borel subsets A ⊂ [0, 1]: • either there exists a homeomorphism φ ∈ Hsuch that the image φ(A) contains no 3-term arithmetic progressions; • or, for every φ ∈ H, the image φ(A) contains arithmetic progressions of arbitrary finite length. In fact, we show that the first alternative holds if and only if the set A is meager (a countable union of nowhere dense sets).en_US
dc.identifier.citationBoshernitzan, Michael and Chaika, Jon. "Dichotomy for arithmetic progressions in subsets of reals." <i>Proceedings of the American Mathematical Society,</i> 144, (2016) American Mathematical Society: 5029-5034. http://dx.doi.org/10.1090/proc/13273.en_US
dc.identifier.doihttp://dx.doi.org/10.1090/proc/13273en_US
dc.identifier.urihttps://hdl.handle.net/1911/94346en_US
dc.language.isoengen_US
dc.publisherAmerican Mathematical Societyen_US
dc.rightsArticle is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.en_US
dc.titleDichotomy for arithmetic progressions in subsets of realsen_US
dc.typeJournal articleen_US
dc.type.dcmiTexten_US
dc.type.publicationpublisher versionen_US
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