Definition:Section of Étalé Space/Definition 2

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 mapping $s : U \to \operatorname{\acute Et} \left({\mathcal F}\right)$ such that for all $x \in U$ there exists an open neighborhhood $V$ of $x$ in $U$ such that the restriction of $s$ to $V$ is the section associated to some $t \in \mathcal F \left({V}\right)$.

Also see

 * Equivalence of Definitions of Section of Étalé Space