Let $M\subset\mathbb R^n$. Then $M$ is an embedded $m$-dimensional manifold if for all $x\in M$, there exists a neighborhood $U \subset\mathbb R^n$ of $x$ and a smooth function $f:U\to\mathbb R^{n-m}$ such that $M\cap U = f^{-1}(0)$ and $Df(y):\mathbb R^n\to\mathbb R^{n-m}$ is surjective for all $y \in U$.
Wikidata ID: Q203920