New Results in the Theory of Packing and Covering

Let J be a system of sets. If all members of J are contained in a given set C and each point of C belongs to at most one member of J then J is said to be a packing into C. If, on the other hand, each point of C belongs to at least one member of J then we say that J is a covering of C. Packings and coverings have been considered in various spaces and on various combinatorial structures. Here we are interested in problems concerning packings and coverings consisting of convex bodies in spaces of constant curvature, i.e. in Euclidean, spherical and hyperbolic space. Instead of saying that J is a packing into the whole space or J is a covering of the whole space we shall simply use the terms J is a packing and J is a covering.

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