Definition:Section (Topology)

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

 * Definition:Fiber Bundle