submersion

A differentiable map $f:X\to Y$ differential manifolds $X$ and $Y$ is called a submersion at a point $x\in X$ if the tangent map

$$\mathrm{T}f(x):\mathrm{T}X(x)\to \mathrm{T}Y(f(x))$$

between the tangent spaces of $X$ and $Y$ at $x$ and $f(x)$ is surjective.

If $f$ is a submersion at every point of $X$, then $f$ is called a submersion. A submersion $f:X\to Y$ is an open mapping, and its image is an open submanifold of $Y$.

A fibre bundle $p:X\to B$ over a manifold $B$ is an example of a submersion.