Definition:Sheaf of Sets on Topological Space

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

Let $\map {\mathbf {Ouv} } T$ be the category of open sets of $T$.

Let $\map {\mathbf {Ouv} } T^{\mathrm {op} }$ be the dual category of $\map {\mathbf {Ouv} } T$.

Let $\mathbf {Set}$ be the category of sets.

Let $\FF : \map {\mathbf {Ouv} } T^{\mathrm {op} } \to \mathbf {Set}$ be a presheaf of sets on $T$.

Also see

 * Equivalence of Definitions of Sheaf of Sets
 * Sheaf of Sets iff Set-Valued Sheaf
 * Definition:Sheaf on Topological Space