On OM-decomposable sets

We introduce and study the family of sets in a finite-dimensional Euclidean space which can be written as the Minkowski sum of an open, bounded, and convex set and a closed convex cone. We establish several properties of the class of such sets, called OM-decomposable, some of which extend related properties holding for the class of Motzkin decomposable sets (i.e., those for which the convex and bounded set in the decomposition is requested to be closed, hence compact).