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Sets Meeting Isometric Copies of the Lattice Z2 in Exactly One Point

Steve Jackson and R. Daniel Mauldin
Proceedings of the National Academy of Sciences of the United States of America
Vol. 99, No. 25 (Dec. 10, 2002), pp. 15883-15887
Stable URL: http://www.jstor.org/stable/3073876
Page Count: 5
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Sets Meeting Isometric Copies of the Lattice Z2 in Exactly One Point
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Abstract

The construction of a subset S of R2 such that each isometric copy of Z2 (the lattice points in the plane) meets S in exactly one point is indicated. This provides a positive answer to a problem of H. Steinhaus [Sierpiński, W. (1958) Fund. Math. 46, 191-194].

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