Definition:Section of Étalé Space/Definition 1

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 continuous mapping $s: U \to \map {\operatorname {\acute Et} } {\mathcal F}$ such that:
 * $\pi \circ s = I_U$

where $I_U$ is the identity mapping on $U$.

Also see

 * Equivalence of Definitions of Section of Étalé Space