A note on sets having the Steinhaus property


A planar set is said to have the Steinhaus property if however it is placed on R<sup>2</sup>, it contains exactly one integer lattice point. The main result proved in this note is that if a set S satisfying the Steinhaus proper- contains a circle of positive radius, then it contains the disk enclosed by the circle. A result of Mihai Ciucu [2] would then imply that any set having the Steinhaus property cannot contain a circle of positive radius in it.

DOI Code: 10.1285/i15900932v16n1p77

Keywords: Geometry of numbers; Steinhaus property

Classification: 11H16

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