Constant sheaf of sets
= Constant sheaf of sets
{title2=$\Delta T(U)=\operatorname{LC}(U,T)$}
The sections are <locally constant functions> into a discrete set $T$, with ordinary restriction. It is the <sheafification> of the <constant presheaf of sets>. Its value on an empty open set is a singleton, even if $T$ is empty. For a topological space, this construction is <left adjoint> to the <global sections functor>: a map from it to a sheaf is a family of global sections indexed by $T$.