Definition:Associated Section of Étalé Space

Definition
Let $X$ be a topological space.

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

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

Let $U\subseteq X$ be open.

Let $s\in \mathcal F(U)$ be a section.

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

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

Also see

 * Definition:Section of Étalé Space