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## Main Question or Discussion Point

Is there a C^infty map that is one to one from R^n to R?

Thanks.

Thanks.

- Thread starter mathsq
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Is there a C^infty map that is one to one from R^n to R?

Thanks.

Thanks.

- #2

Bacle2

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I think no, but I have no proof. By invariance of domain, the map cannot be onto, since ℝ

ℝ that is open in ℝ

Or, you can use Sard's theorem (we had a similar problem here a while back): Since every point in ℝ

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Bacle2

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Thank you! That makes sense.

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mathwonk

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