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