ScalingStacks

Definition 2.83. Let $Z=\spec(A_{Z})$ be an affine $k$-scheme of finite type, where $A_{Z}$ is a $k$-algebra of finite type. Its Berkovich analytification $Z^{an}$ is the topological space constituting of all multiplicative seminorms $\vvvert\mathord{\cdot}\vvvert$ on $A_{Z}$ as points and with the canonical topology (the weakest topology making every function $\vvvert\mathord{\cdot}\vvvert\to\vvvert f\vvvert$ continuous for each $f\in A_{Z}$). ([Ber, Remark 3.4.2])