Some results about nondominated solutions

We will prove that, in the case where all the domination cones are closed and convex, have a nonempty interior, and are totally ordered with respect to inclusion, the set of weakly nondominated outcomes of a nonempty convex compact setY R ⁿ is connected. Further, we give a relationship between weakly nondominated and nondominated solutions.The author would like to thank the referees for their valuable comments.