\begin{definition}[Definition:Sheaf of Sets on Topological Space/Definition 2]
Let $T = \struct {S, \tau}$ be a topological space.
Let $\FF : \map {\mathbf {Ouv} } T ^{\mathrm {op} } \to \mathbf {Set}$ be a presheaf of sets on $T$.
Let $\map {\operatorname {Sp\acute e} } \FF$ be the étalé space of $\FF$.
Let $\FF'$ be the sheaf of sections of $\map {\operatorname {Sp \acute e} } \FF \to T$.
$\FF$ is a '''sheaf of sets''' on $T$ {{iff}} the canonical mapping $\FF \to \FF'$ is an isomorphism.
\end{definition}