- Home
- →
- Research Collections
- →
- Interdisciplinary and Peer-Reviewed
- →
- View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.
| 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 |
