# Definition:Section (Topology)

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## Contents

## Definition

Let $M, E$ be topological spaces.

Let $\pi: E \to M$ be a continuous surjection.

Let $I_M: M \to M$ be the identity mapping on $M$.

Then a **section** of $E$ is a continuous mapping $s: M \to E$ such that $\pi \circ s = I_M$.

## Also known as

Some authors use the word **cross section** as opposed to section.

## Also see

## Sources

- 2003: John M. Lee:
*Introduction to Smooth Manifolds*: $\S 10$: Local and Global Sections of Vector Bundles