Constructible topology

In commutative algebra, the constructible topology on the spectrum ${\displaystyle \operatorname {Spec} (A)}$ of a commutative ring ${\displaystyle A}$ is a topology where each closed set is the image of ${\displaystyle \operatorname {Spec} (B)}$ in ${\displaystyle \operatorname {Spec} (A)}$ for some algebra B over A. An important feature of this construction is that the map ${\displaystyle \operatorname {Spec} (B)\to \operatorname {Spec} (A)}$ is a closed map with respect to the constructible topology.

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