Let G be a real algebraic unipotent group and let Lambda be a lattice in G, with p:G->G/Lambda the quotient map. Given a definable subset X of G, in some o-minimal expansion of the reals, we describe the closure of p(X) in G/Lambda in terms definable families of cosets of real algebraic subgroups of G of positive dimension. The family is extracted from X independently of Lambda.