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The spectrum of a commutative ring \(R\), \(\mathrm{Spec}(R)\), is the set of all its prime ideals. The spectrum may be made into a topological space by endowing it with the Zariski topology - the closed sets are given by \(V_I:=\{\mathfrak{p}\in\mathrm{Spec}(R)|I\subseteq\mathfrak{p}\}\), where \(I\) is any ideal of \(R\). In this way, \(\mathrm{Spec}\) is a contravariant functor from \(\mathbf{CRing}\) to \(\mathbf{Set}\), as any ring homomorphism \(\phi:R\to S\) induces a map \(\mathfrak{p}\mapsto \phi^{-1}(\mathfrak{p})\) which is continuous with respect to this topology.