A 
-space is a topological
space fulfilling the T1-separation
axiom: For any two distinct points 
there exist two open sets 
and 
such that 
and 
, and 
and 
. In the terminology of Alexandroff and Hopf (1972),
-spaces are known as Fréchet
spaces (though this is confusing and nonstandard).
A standard example of a 
-space
is the set of integers with the
cofinite topology. Its open
sets are the empty set and the subsets
with finite complements.
It is closed under finite intersection and arbitrary
union so is a topology. Any
integer's complement is
an open set, so given two integers
and using their complements as open
sets, it follows that the 
definition is satisfied. Some 
-spaces are not T2-spaces.
