Section of a fiber bundle ($\pi \circ s={\mathrm{id}}_B$)

A section of a fiber bundle $\pi :E\to B$ is a continuous map $s:B\to E$ with $\pi \circ s={\mathrm{id}}_B$. It chooses a point of each fibre continuously. A section of a vector bundle is the special case for vector fibres; a projective bundle section chooses a line in each fibre of the underlying vector bundle.