# Whitney Immersion Theorem

## Contents

## 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.