The answer on this question says that, for $A$ a ring and a multiplicative subset $S \subset A$, then $\operatorname{Spec}(S^{-1}A)$ is homeomorphic to a subset of $\operatorname{Spec}(A)$, I assume via the map $f : \operatorname{Spec}(S^{-1}A) \rightarrow \operatorname{Spec}(A)$ induced from the localization map $A\rightarrow S^{-1}A$.
Already I understand why $f$ is a continuous injective map.
I was wondering if anyone could suggest a reference that describes how to show $f$ is also a homeomorphism onto its image?
