The notion of a homogeneous covering of a given set is introduced and examined. Some homogeneous coverings of a Euclidean space, consisting of pairwise congruent geometric figures (spheres, hyperplanes, etc.), are constructed using the method of transfinite induction.
Homogeneous covering, Euclidean space, sphere, hyperplane, transfinite induction.
MSC 2000: 03E75, 05B40, 52C17.