A remark on sets having the Steinhaus property

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dc.contributor.author Ciucu, Mihai en_US
dc.date.accessioned 2006-09-11T19:27:28Z
dc.date.available 2006-09-11T19:27:28Z
dc.date.issued 1996-09 en_US
dc.identifier.citation Ciucu, Mihai; (1996). "A remark on sets having the Steinhaus property." Combinatorica 16(3): 321-324. <http://hdl.handle.net/2027.42/47844> en_US
dc.identifier.issn 1439-6912 en_US
dc.identifier.issn 0209-9683 en_US
dc.identifier.uri http://hdl.handle.net/2027.42/47844
dc.description.abstract A point set satisfies the Steinhaus property if no matter how it is placed on a plane, it covers exactly one integer lattice point. Whether or not such a set exists, is an open problem. Beck has proved [1] that any bounded set satisfying the Steinhaus property is not Lebesgue measurable. We show that any such set (bounded or not) must have empty interior. As a corollary, we deduce that closed sets do not have the Steinhaus property, fact noted by Sierpinski [3] under the additional assumption of boundedness. en_US
dc.format.extent 194544 bytes
dc.format.extent 3115 bytes
dc.format.mimetype application/pdf
dc.format.mimetype text/plain
dc.language.iso en_US
dc.publisher Springer-Verlag; Akadémiai Kiadó en_US
dc.subject.other Mathematics, General en_US
dc.subject.other Mathematics en_US
dc.subject.other 52 C 15 en_US
dc.subject.other 05 B 40 en_US
dc.subject.other Combinatorics en_US
dc.subject.other 11 H 16 en_US
dc.title A remark on sets having the Steinhaus property en_US
dc.type Article en_US
dc.subject.hlbsecondlevel Mathematics en_US
dc.subject.hlbtoplevel Science en_US
dc.description.peerreviewed Peer Reviewed en_US
dc.contributor.affiliationum Department of Mathematics, University of Michigan, 48109-1003, Ann Arbor, Michigan en_US
dc.contributor.affiliationumcampus Ann Arbor en_US
dc.description.bitstreamurl http://deepblue.lib.umich.edu/bitstream/2027.42/47844/1/493_2005_Article_BF01261317.pdf en_US
dc.identifier.doi http://dx.doi.org/10.1007/BF01261317 en_US
dc.identifier.source Combinatorica en_US
dc.owningcollname Interdisciplinary and Peer-Reviewed
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