Definition:Submersion

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

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

Let $df_x: T_x \left({X}\right) \to T_y \left({Y}\right)$ be a surjection.

Then $f$ is a submersion of $X$ on $Y$.