Flavors of translative coverings (Q2417590)

This is a survey on results and methods on covering in \(\mathbb{R}^n\). The author discusses several problems related to covering, such as covering of the whole space and the Rogers theorem, covering by a sequence of sets, covering of a convex body by translates of another one, covering the sphere by caps, the illumination problem and fractional illumination, the Borsuk problem, \(m\)-fold coverings, the problem of decomposability of multiple coverings, the Sudakov inequality and its dual, duality of covering numbers. The author presents the ideas of proofs as well, in particular, he outlines four approaches to the Rogers theorem. For the entire collection see [Zbl 1411.52002].