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Homesubmersion

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# submersion

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

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

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 $f\colon X\to Y$ is an open mapping, and its image is an open submanifold of $Y$.

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

Related:

Immersion

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

53-00*no label found*57R50

*no label found*

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