\begin{definition}[Definition:Embedding (Differential Geometry)]
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''' {{iff}} $f$ is:
:injective
:a $C^k$-immersion
:a homeomorphism on its image
\end{definition}