Let M⊂RnM\subset\mathbb R^nM⊂Rn. Then MMM is an embedded mmm-dimensional manifold if for all x∈Mx\in Mx∈M, there exists a neighborhood U⊂RnU \subset\mathbb R^nU⊂Rn of xxx and a smooth function f:U→Rn−mf:U\to\mathbb R^{n-m}f:U→Rn−m such that M∩U=f−1(0)M\cap U = f^{-1}(0)M∩U=f−1(0) and Df(y):Rn→Rn−mDf(y):\mathbb R^n\to\mathbb R^{n-m}Df(y):Rn→Rn−m is surjective for all y∈Uy \in Uy∈U.
Wikidata ID: Q203920