Definition:Associated Section of Étalé Space

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

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

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

Let $U \subseteq S$ be open in $T$.

Let $s \in \mathcal F \left({U}\right)$ be a section.

The associated section of $\operatorname {\acute Et} \left({\mathcal F}\right)$ is the mapping:
 * $\overline s : U \to \operatorname {\acute Et} \left({\mathcal F}\right) : x \mapsto \left({x, s_x}\right)$

where $s_x$ is the image in the stalk at $x$.

Also see

 * Definition:Section of Étalé Space