Definition:Section of Étalé Space/Definition 2

Definition
Let $T = \struct {S, \tau}$ be a topological space.

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

Let $\struct {\map {\operatorname{\acute Et} } {\mathcal F}, \pi}$ be its étalé space.

Let $U \subseteq S$ be open.

A section of $\map {\operatorname {\acute Et} } {\mathcal F}$ on $U$ is a mapping $s: U \to \map {\operatorname {\acute Et} } {\mathcal F}$ 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 $t \in \map {\mathcal F} V$.

Also see

 * Equivalence of Definitions of Section of Étalé Space