  In this paper, we investigate the topological structure of solution sets of
monotone vector variational inequalities. We show that if the weak Pareto
solution set of a monotone vector variational inequality is disconnected, then
each connected component of the set is unbounded. Similarly, this property
holds for the proper Pareto solution set. Two open questions on the topological
structure of the solution sets of (symmetric) monotone vector variational
inequalities are raised at the end of the paper.
