The prime ideals of a ring can be endowed with the Zariski topology.
This is done by defining a function which maps ideals of to
closed sets (see for example zarcls0 for the definition of ).
The closed sets of the topology are in the range of (see zartopon).
The correspondence with the open sets is made in zarcls.
As proved in zart0, the Zariski topology is T0 , but generally not T1 .