Let $A$ be a complex abelian variety and $\pi\colon \mathbb{C}^n\to A$

be the covering map.

In this talk we consider the topological closure $\pi(X)$ of an

algebraic subvariety $X$ of $\mathbb{C}^n$ and describe it in terms of

finitely many algebraic families of cosets of real subtori.

We also obtain a similar description when $A$ is a real torus and

$X$ is a

subset of $\mathbb{R}^n$ definable in an o-minimal structure.

Joint work with Y. Peterzil