# Definition:Embedding (Differential Geometry)

## Definition

Let $m,n\geq1$ be natural numbers.

Let $U\subset\R^n$ be open.

Let $f : U \to \R^m$ be a mapping.

Then $f$ is a $C^k$-embedding if and only if $f$ is:

### Rank

The rank of an embedding is the rank of its differential at any point.