# Question on the Möbius Strip

If we define the Möbius strip by a relation, $R$, by $(1,y)R(-1,-y)$ on the space $I^2$ how can one prove that it is homeomorphic to a subset of $\Bbb R^3$?

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There are many realizations of the Möbius strip into $\mathbb{R}^3$ as an image of $I^2$. For example, here.
Try looking for a theorem that proves that such functions have continuous local inverses when their Jacobian has full rank everywhere. I was thinking about the gluing along the edges, and it might be less tedious to map from $\mathbb{R}^2$ to $\mathbb{R^3}$ factoring through $\mathbb{R}^2/I^2$. –  alex.jordan Apr 17 '13 at 15:26