Definition:Submersion

Let $$X$$ and $$Y$$ be manifolds, with $$\dim X \ge \dim Y$$.

Let $$f: X \to Y$$ be smooth and $$f(x)=y$$.

If $$df_x: T_x(X) \to T_y(Y)$$ is onto, $$f$$ is called a submersion of $$X$$ on $$Y$$.