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A remark on sets having the Steinhaus property

dc.contributor.authorCiucu, Mihaien_US
dc.date.accessioned2006-09-11T19:27:28Z
dc.date.available2006-09-11T19:27:28Z
dc.date.issued1996-09en_US
dc.identifier.citationCiucu, 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.issn1439-6912en_US
dc.identifier.issn0209-9683en_US
dc.identifier.urihttps://hdl.handle.net/2027.42/47844
dc.description.abstractA 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.extent194544 bytes
dc.format.extent3115 bytes
dc.format.mimetypeapplication/pdf
dc.format.mimetypetext/plain
dc.language.isoen_US
dc.publisherSpringer-Verlag; Akadémiai Kiadóen_US
dc.subject.otherMathematics, Generalen_US
dc.subject.otherMathematicsen_US
dc.subject.other52 C 15en_US
dc.subject.other05 B 40en_US
dc.subject.otherCombinatoricsen_US
dc.subject.other11 H 16en_US
dc.titleA remark on sets having the Steinhaus propertyen_US
dc.typeArticleen_US
dc.subject.hlbsecondlevelMathematicsen_US
dc.subject.hlbtoplevelScienceen_US
dc.description.peerreviewedPeer Revieweden_US
dc.contributor.affiliationumDepartment of Mathematics, University of Michigan, 48109-1003, Ann Arbor, Michiganen_US
dc.contributor.affiliationumcampusAnn Arboren_US
dc.description.bitstreamurlhttp://deepblue.lib.umich.edu/bitstream/2027.42/47844/1/493_2005_Article_BF01261317.pdfen_US
dc.identifier.doihttp://dx.doi.org/10.1007/BF01261317en_US
dc.identifier.sourceCombinatoricaen_US
dc.owningcollnameInterdisciplinary and Peer-Reviewed


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