(Evaluation maps) A point $x$ of $Spec^{an}(R/K)$ is an equivalence class of homomorphisms of $K$-algebras

$$eval_{x}\,:\,R\to K_{x}\,\,,$$

where $K_{x}\supset K$ is a complete field equipped with a non-archimedean valuation, which extends the valuation $val_{K}$, and such that $K_{x}$ is generated by the closure of the image of $eval_{x}$.