Definition:Embedding (Differential Geometry)

Definition
Let $m, n \ge 1$ 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 $f$ is:
 * injective
 * a $C^k$-immersion
 * a homeomorphism on its image

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

Also see

 * Definition:Immersion
 * Definition:Submersion