Some generalization of Steinhaus' lattice points problem
Tom 123 / 2011
Colloquium Mathematicum 123 (2011), 129-132 MSC: 46C15, 54E52. DOI: 10.4064/cm123-1-9
Steinhaus' lattice points problem addresses the question of whether it is possible to cover exactly $n$ lattice points on the plane with an open ball for every fixed nonnegative integer $n$. This paper includes a theorem which can be used to solve the general problem of covering elements of so-called quasi-finite sets in Hilbert spaces. Some applications of this theorem are considered.