Whitney Immersion Theorem

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Theorem

Let $m > 1$ be a natural number.


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


Corollary

Let $m \in \N$.


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


Proof


Source of Name

This entry was named for Hassler Whitney.