Constructible topology
In commutative algebra, the constructible topology on the spectrum Spec ( A ) {\displaystyle \operatorname {Spec} (A)} of a commutative ring A {\displaystyle A} is a topology where each closed set is the image of Spec ( B ) {\displaystyle \operatorname {Spec} (B)} in Spec ( A ) {\displaystyle \operatorname {Spec} (A)} for some algebra B over A. An important feature of this construction is that the map Spec ( B ) → Spec ( A ) {\displaystyle \operatorname {Spec} (B)\to \operatorname {Spec} (A)} is a closed map with respect to the constructible topology. With respect to this topology, Spec ( A ) {\displaystyle \operatorname {Spec} (A)} is a compact, Hausdorff, and totally disconnected topological space (i.e., a Stone space).