  B. Mazur has considered the question of density in the Euclidean topology of
the set of ${\Bbb Q}$-rational points on a variety $X$ defined over ${\Bbb Q}$,
in particular for Abelian varieties. In this paper we consider the question of
closures of the image of finitely generated subgroups of $T({\Bbb Q})$ in
$\Gamma \backslash T({\Bbb R})$ where $T$ is a torus defined over ${\Bbb Q}$,
$\Gamma$ an arithmetic subgroup such that $\Gamma \backslash T({\Bbb R})$ is
compact. Assuming Schanuel's conjecture, we prove that the closures correspond
to sub {\it algebraic} tori of $T$.
