Coordinate Charts and inverse of functions.

Hello,

i have a question about this situation. Let denote $\displaystyle T^2=S^1 \times S^1$ the Torus.

And let $\displaystyle f:\mathbb{R}^2 \rightarrow T^2$ be the projection defined by

$\displaystyle f(x,y)=(e^{i2\pi x},e^{i2\pi y})$.

The claim is now, if $\displaystyle \phi$ is a chart for $\displaystyle \mathbb{R}^2$ , s.t. $\displaystyle f_{|dom\phi}$ is injective, then $\displaystyle \phi \circ (f_{|dom\phi})^{-1}$ is a chart for $\displaystyle T^2$.

i don't understand why the composition is a chart?

Can you help me?

Regards