Abstract: Discuss globally proper effective point sets connectivity in locally convex topological linear space. In the case that the feasible domain is a general compact subset that is non-empty, the target set value mapping on the constraint set is upper semi-continuous and cone-like convex, and the constraint mapping is upper semi-continuous. By proving the connectedness of set-valued maps on dual cones, a nonempty connectivity theorem for global effective point set for set-valued optimization problems with constrained cone-like convex is presented. This conclusion is obtained under relatively weak conditions, which further expands the current related conclusions on connectivity of global true efficient point sets.