Jacobson topology

Summary

The Jacobson topology, or hull-kernel topology, is a topology on the set $\operatorname{Prim}(R)$ of primitive ideals of a ring $R$. A set of primitive ideals is closed when it consists of all primitive ideals that contain some fixed ideal. For a commutative ring it is the Zariski topology restricted to maximal ideals. So the space $\operatorname{Prim}(R)$ is a noncommutative analogue of the spectrum of a ring. For a commutative C*-algebra $C_0(X)$ it recovers the space $X$. For this reason it is the standard topology on the primitive spectrum of a C*-algebra.