Let $W_1,W_2 \subset \mathbb R^n$ be open. A function $g: W_1\to W_2$ is a $C^k$-embedding if $g$ is injective, $g$ is of class $C^k$, and the total derivative $Dg(x)$ is invertible for all $x \in W_1$.
Wikidata ID: Q980509