the problem I am dealing with is part of a three step problem in order to show how the affine line $\mathbb{A}_R^1 = Spec(R[t])$ for a PID $R$ looks like. The problem has been dealt with a lot here on stack exchange, but my question is related to a specific part of the solution. Namely, let $\pi:\mathbb{A}_R^1\rightarrow Spec(R)$ be the projection associated to the canonical injection $R\rightarrow R[t]$.
Given a point $s\in Spec(R)$, the fiber $\pi^{-1}(s)$ is canonically homeomorphic to the affine line $\mathbb{A}_{k(s)}^1$, where $k(s)$ is the residue field of $s$.
So I guess this is a fairly trivial fact but I just don't see it. Can anyone help me out?