\begin{definition}[Definition:Section of Étalé Space/Definition 2]
Let $T = \struct {S, \tau}$ be a topological space.
Let $\FF$ be a presheaf of sets on $T$.
Let $\struct {\map {\mathrm {\acute Et} } \FF, \pi}$ be its étalé space.
Let $U \subseteq S$ be open.
A '''section''' of $\map {\mathrm {\acute Et} } \FF$ on $U$ is a mapping $s: U \to \map {\mathrm {\acute Et} } \FF$ 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 $t \in \map \FF V$.
\end{definition}