On a lattice problem of H. Steinhaus
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- by Steve Jackson and R. Daniel Mauldin
- J. Amer. Math. Soc. 15 (2002), 817-856
- DOI: https://doi.org/10.1090/S0894-0347-02-00400-9
- Published electronically: June 13, 2002
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Abstract:
It is shown that there is a subset $S$ of $\mathbb {R}^2$ such that each isometric copy of $\mathbb {Z}^2$ (the lattice points in the plane) meets $S$ in exactly one point. This provides a positive answer to a problem of H. Steinhaus.References
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Bibliographic Information
- Steve Jackson
- Affiliation: Department of Mathematics, University of North Texas, Denton, Texas 76203
- MR Author ID: 255886
- ORCID: 0000-0002-2399-0129
- Email: jackson@unt.edu
- R. Daniel Mauldin
- Affiliation: Department of Mathematics, University of North Texas, Denton, Texas 76203
- Email: mauldin@unt.edu
- Received by editor(s): February 14, 2001
- Received by editor(s) in revised form: October 29, 2001
- Published electronically: June 13, 2002
- Additional Notes: The first author’s research was supported by NSF Grant DMS-0097181.
The second author’s research was supported by NSF Grant DMS-9801583 - © Copyright 2002 American Mathematical Society
- Journal: J. Amer. Math. Soc. 15 (2002), 817-856
- MSC (2000): Primary 04A20; Secondary 11H31
- DOI: https://doi.org/10.1090/S0894-0347-02-00400-9
- MathSciNet review: 1915820