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In this paper, we deal with connectedness of the approximate solution sets for set optimization problems by using the scalarization method. We first obtain two scalarization results for the sets of  l -minimal approximate solutions and weak  l -minimal approximate solutions for set optimization problems without using the convexity of the objective mapping and the separation theorem of convex sets. Then, we establish connectedness of the sets of  l -minimal approximate solutions and weak  l -minimal approximate solutions for set optimization problems by utilizing the scalarization results. Finally, we derive arcwise connectedness of the set of weak  l -minimal approximate solutions for set optimization problems.

Connectedness of the approximate solution sets for set optimization problems