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Some generalization of Steinhaus' lattice points problem

Paweł Zwoleński (2011)

Colloquium Mathematicae

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.

Some geometric properties of typical compact convex sets in Hilbert spaces

F. de Blasi (1999)

Studia Mathematica

An investigation is carried out of the compact convex sets X in an infinite-dimensional separable Hilbert space , for which the metric antiprojection q X ( e ) from e to X has fixed cardinality n+1 ( n arbitrary) for every e in a dense subset of . A similar study is performed in the case of the metric projection p X ( e ) from e to X where X is a compact subset of .

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