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is $M=\{ (\cos t,\cos2t):t\in \mathbb{R}\}$ a differential manifold

I know that for small intervals is manifold(is a parabola), but in all $\mathbb{R}$ i dont know

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    I think you're right. It's just a piece of parabola bounded by the square $[-1, 1]^2$.2012-11-27
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    Do you allow your manifolds to have boundary?2012-11-27

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