On the Characterization of some Families of Closed Convex Sets

This paper deals with the characterization of the sums of compact convex sets with linear subspaces, simplices, sandwiches (convex hulls of pairs of parallel ane manifolds) and parallelotopes in terms of the so-called internal and conical representations, topological and geometrical properties. In particular, it is shown that a closed convex set is a sandwich if and only if its relative boundary is unconnected. The characterizations of families of closed convex sets can be useful in dierent