Continuity properties of solutions of vector optimization

This paper characterizes upper semicontinuity and lower semicontinuity of weakly efficient solution mapping SwSw and efficient solution mapping S   on the space Cm(X)Cm(X) of continuous mm-dimension-vector-real-valued objective functions on a nonempty compact set X. As applications, some more interesting results about the properties of weakly efficient solutions and efficient solutions are obtained, such as the upper semicontinuity of S at f   in Cm(X)Cm(X) implies the closedness and connectedness of the set S(f)S(f) of efficient solutions, any essential weakly efficient solution of f can be approximated by a sequence of efficient solutions of f   (i.e., Ew(f)⊂S(f)¯), and in the sense of Baire categories “most” of vector optimization problems in Cm(X)Cm(X) for efficient solutions are essential, and so on.