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how do I show that $S^1 \times S^1 \ldots \times S^1 $ is diffeomorphic to $\mathbb{T}^n$ as manifolds? Where $S^1 \times S^1 \ldots \times S^1 $ has the natural differential structure of a product manifold and $\mathbb{T}^n$ is obtained by the action of the group of integer translation of $\mathbb{R}^n$ in $\mathbb{R}^n$

ADDED(04/05/12):

I defined $f$ as in comments, proved that it is a bijection, and stuck here...

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    Dear Jr., it is better if you write down *everything* you have done in the body of the question. It allows us to help you exactly at the point you got stuck (and avoids our having to ask 25 questions to find where that point is!)2012-04-05

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