  We investigate the relation between the convergence of a sequence of lattices
and the set-theoretic convergence of their corresponding Voronoi cells
sequence. We prove that if a sequence of full rank lattices converges to a full
rank lattice, then the closures of the limit infimum and limit supremum of the
Voronoi cells converges to the corresponding Voronoi cell. It remains an open
question if the converse is also true.
