Weakly Motzkin Predecomposable Sets

摘要

We introduce and study the class of weakly Motzkin predecomposable sets, which are those sets in R-n that can be expressed as the Minkowski sum of a bounded convex set and a convex cone, none of them being necessarily closed. This class contains that of Motzkin predecomposable sets, for which the bounded components are compact, which in turn contains the class of Motzkin decomposable sets, for which the bounded components are compact and the conic components are closed.