Definition:Submersion

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

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

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