Sheaf of continuous functions

This article describes a sheaf on a manifold (the manifold may possess some additional structure in terms of which the sheaf is defined)
View other sheaves on manifolds

Definition

Let $M$ be a topological manifold (or more generally, any topological space). The sheaf of continuous functions on $M$ is defined as follows:

• To every open subset $U$ of $M$, we associate the $\mathbb{R}$-algebra of continuous real-valued functions on $U$
• The restriction map is simply function restriction

Related notions

• Sheaf of multiply differentiable functions
• Sheaf of infinitely differentiable functions
• Sheaf of real-analytic functions