Constant Sheaf - Basics

Basics

Let X be a topological space, and A a set. The sections of the constant sheaf A over an open set U may be interpreted as the continuous functions U → A, where A is given the discrete topology. If U is connected, then these locally constant functions are constant. If f: X → {pt} is the unique map to the one-point space and A is considered as a sheaf on {pt}, then the inverse image f−1A is the constant sheaf A on X. The sheaf space of A is the projection map X × A → X (where A is given the discrete topology).