What is the leaf space of the Kronecker foliation of the torus?

Question

The leaves of the Kronecker foliation of the torus are diffeomorphic to the real line $\mathbb{R}$ and are dense on $T^2$. I cannot, however, describe what is the leaf space $T^2/\mathcal{F}$.

Answer 1

If every leaf is dense, every point in the leaf space lies in the closure of any other point. This characterises the co-discrete space.