Whitney Immersion Theorem

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Theorem

For $m > 1$, any smooth $m$-dimensional manifold can be immersed in Euclidean $\left({2m-1}\right)$-space.


Equivalently, every smooth $m$-dimensional manifold can be immersed in the $\left({2m-1}\right)$-dimensional sphere.

This latter statement thus removes the constraint that $m > 1$.


Proof


Source of Name

This entry was named for Hassler Whitney.