Definition:Section of Étalé Space/Definition 1

Definition
Let $T = \left({S, \tau}\right)$ be a topological space.

Let $\mathcal F$ be a presheaf of sets on $T$.

Let $\left({\operatorname{\acute Et} \left({\mathcal F}\right), \pi}\right)$ be its étalé space.

Let $U \subseteq S$ be open.

A section of $\operatorname{\acute Et} \left({\mathcal F}\right)$ on $U$ is a continuous mapping $s : U \to \operatorname{\acute Et} \left({\mathcal F}\right)$ such that $\pi \circ s = \operatorname{id}_U$, where $ \operatorname{id}_U$ is the identity mapping on $U$.

Also see

 * Equivalence of Definitions of Section of Étalé Space