Strategy-proofness of continuous aggregation maps

We consider continuous aggregation maps (e.g., social welfare functions). By assuming that the voters have preferences over social outcomes, we regard the social decision procedure as a noncooperative game, with the aggregation map as a game form. The map is called strategy-proof if it is a Nash equilibrium that the voters report their most preferred outcomes. We give sufficient topological conditions on the space of outcomes so that only dictatorial maps are strategy-proof.