Definition:Section (Topology)

Definition
Let $M, E$ be topological spaces.

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

Let $\mathrm{Id}_M : M \to M$ be the identity mapping on $M$.

Then a section of $E$ is a continuous mapping $s : M \to E$ with $\pi \circ s = \mathrm{Id}_M $.

Also known as
Some authors use the word cross section as opposed to section.

Also See

 * Definition:Fiber Bundle