A sheaf on a topological space 
is a presheaf 
whose local sections can be uniquely glued. More precisely,
for every open covering 
of an open set 
,
it satisfies the following conditions:
1. If two sections 
have the same restriction to every 
, then 
.
2. If sections 
agree on every overlap 
,
then there is a section 
whose restriction to each 
is 
.
For example, let 
be a variety over a field 
.
If 
denotes the ring of regular functions
from 
to 
then with the usual restrictions 
is a sheaf which is called the sheaf of regular functions
on 
.
In the same way, one can define the sheaf of continuous real-valued functions on any topological space, and also for differentiable functions.
