Sets meeting isometric copies of the lattice Z2 in exactly one point.

Jackson, Steve; Mauldin, R Daniel · Proc Natl Acad Sci U S A · 2002

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Abstract

The construction of a subset S of (2) such that each isometric copy of (2) (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].