# Sheaf of continuous functions

From Diffgeom

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

- To every open subset of , we associate the -algebra of continuous real-valued functions on
- The restriction map is simply function restriction