If 
is any compact space, let 
be a subalgebra of the algebra 
over the reals 
with binary operations 
and 
. Then, if 
contains the constant functions and separates the points of
(i.e., for any two distinct points 
and 
of 
, there is some function 
in 
such that 
), 
is dense in 
equipped with the uniform norm.
This theorem is a generalization of the Weierstrass approximation theorem.
