“…As is shown in Roos and Noltemeier [14], dynamic Voronoi diagrams change in an entirely continuous fashion. 10 This geometric continuity ensures that, when all the Voronoi edges/faces and Voronoi points of the separate Voronoi diagrams generated at each particular point in time are projected onto each other, the result is a diagram with a full boundary region. Theorem 4.1 should then be more or less obvious once we realize that, first, because the generator regions are connected, from any selection of points from these regions we can reach any other selection of points from those regions by having all points move along continuous trajectories that lie entirely within the generator regions; and second, we can exhaust the possible selections of points from the generator regions by, so to speak, chaining together infinitely many such operations.…”