An embedding result for a class of epigraphical sets and applications to set optimization

We extend to the case of a class of unbounded generalized convex sets, the famous embedding result of Rdstrm.The main motivation for this is to have a new look to epigraphical set-valued maps that are usually involved in set optimization problem.From this point of view, we study several aspects concerning the order of the embedding space induced by the order of the output space of objective mappings.Next, we associate to a set-valued map, an embedding single valued map, and we compare two types of efficiency related to them.Then, some new optimality conditions for set optimization problems are obtained.