If 
is a locally compact T2-space, then the set 
of all continuous complex valued functions on
vanishing at infinity (i.e., for each
, the set 
is compact) equipped with the supremum
norm 
is a commutative 
-algebra.
The Gelfand theorem states that each commutative 
-algebra 
is of the form 
where 
is the maximal ideal space)
of 
.
is unital iff 
is compact.
