Whitney Immersion Theorem

Theorem

Let $m > 1$ be a natural number.

Every smooth $m$-dimensional manifold can be immersed in Euclidean $\paren {2 m - 1}$-space.

Corollary

Let $m \in \N$.

Every smooth $m$-dimensional manifold can be immersed in the $\paren {2 m - 1}$-dimensional sphere.

Proof

This theorem requires a proof. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

Also see

• Weak Whitney Immersion Theorem

Source of Name

This entry was named for Hassler Whitney.