Teoria combinatoria degli insiemi centrati

In two recent papers Komjath and Schmerl consider the combinatorial behaviour of some subsets of the plane called clouds. We extend their results to several subsets of the n-dimensional space, investigating the existence of coverings in relation to some cardinal assumptions on the nature of the continuum. We provide a complete analysis of the subject, and develop a new formulation of Sierpinski's problem in a "local" form.