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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm123-1-9,
author = {Pawe\l\ Zwole\'nski},
title = {Some generalization of Steinhaus' lattice points problem},
journal = {Colloquium Mathematicae},
volume = {122},
year = {2011},
pages = {129-132},
zbl = {1223.46023},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm123-1-9}
}
Paweł Zwoleński. Some generalization of Steinhaus' lattice points problem. Colloquium Mathematicae, Tome 122 (2011) pp. 129-132. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm123-1-9/