A+ CATEGORY SCIENTIFIC UNIT

Some generalization of Steinhaus' lattice points problem

Volume 123 / 2011

Paweł Zwoleński Colloquium Mathematicum 123 (2011), 129-132 MSC: 46C15, 54E52. DOI: 10.4064/cm123-1-9

Abstract

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.

Authors

  • Paweł ZwoleńskiInstitute of Mathematics
    Silesian University
    Bankowa 14
    40-007 Katowice, Poland
    e-mail

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