Lemma 10.17.6. Let $R$ be a ring. Let $f \in R$. The map $R \to R_ f$ induces via the functoriality of $\mathop{\mathrm{Spec}}$ a homeomorphism

$\mathop{\mathrm{Spec}}(R_ f) \longrightarrow D(f) \subset \mathop{\mathrm{Spec}}(R).$

The inverse is given by $\mathfrak p \mapsto \mathfrak p \cdot R_ f$.

Proof. This is a special case of Lemma 10.17.5. $\square$

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