# 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 $\paren {2 m - 1}$-dimensional sphere.

## Proof

## Source of Name

This entry was named for Hassler Whitney.