Some topological properties of solution sets in partially ordered set optimization

In this paper, we study some topological properties, in particular, arcwise connectedness and connectedness of solution sets in set optimization, where the acting space is equipped with partial set order relations.We obtain continuity, generalized convexity, and natural quasi arcwise connectedness of the nonlinear scalarization function and use them to study some topological properties and convergence of efficient and weak efficient solution sets in partially ordered set optimization.We also employ derived results to vector-valued game theory with uncertainty.