Dichotomy for arithmetic progressions in subsets of reals
| dc.citation.firstpage | 5029 | |
| dc.citation.journalTitle | Proceedings of the American Mathematical Society | |
| dc.citation.lastpage | 5034 | |
| dc.citation.volumeNumber | 144 | |
| dc.contributor.author | Boshernitzan, Michael | |
| dc.contributor.author | Chaika, Jon | |
| dc.date.accessioned | 2017-05-22T21:48:43Z | |
| dc.date.available | 2017-05-22T21:48:43Z | |
| dc.date.issued | 2016 | |
| dc.description.abstract | Let 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). | |
| dc.identifier.citation | Boshernitzan, 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. | |
| dc.identifier.doi | http://dx.doi.org/10.1090/proc/13273 | |
| dc.identifier.uri | https://hdl.handle.net/1911/94346 | |
| dc.language.iso | eng | |
| dc.publisher | American Mathematical Society | |
| dc.rights | Article 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. | |
| dc.title | Dichotomy for arithmetic progressions in subsets of reals | |
| dc.type | Journal article | |
| dc.type.dcmi | Text | |
| dc.type.publication | publisher version |
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