Whitney Immersion Theorem

Theorem
For $m > 1$, any smooth $m$-dimensional manifold can be immersed in Euclidean $\left({2m-1}\right)$-space.

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

This latter statement thus removes the constraint that $m > 1$.