Whitney Immersion Theorem

From ProofWiki
Jump to navigation Jump to search

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.