Definition:Associated Section of Étalé Space

Definition

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

Let $\FF$ be a presheaf of sets.

Let $\map {\operatorname {\acute Et} } \FF$ be its étalé space.

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

Let $s \in \map \FF U$ be a section.

The associated section of $\map {\operatorname {\acute Et} } \FF$ is the mapping:

$\overline s : U \to \map {\operatorname {\acute Et} } \FF: x \mapsto \tuple {x, s_x}$

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

Also see

• Definition:Section of Étalé Space