Sets meeting isometric copies of the lattice Z2 in exactly one point.
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].
Jackson
Steve
S
Department of Mathematics, University of North Texas, Denton, TX 76203, USA. jackson@unt.edu
Mauldin
R Daniel
RD