  Extending our insights from \cite{NVOstrowski}, we apply point-free
techniques to sharpen a foundational result in Berkovich geometry. In our
language, given the ring $\mathcal{A}:=K\{R^{-1}T\}$ of convergent power series
over a suitable non-Archimedean field $K$, the points of its Berkovich Spectrum
$\mathcal{M}(\mathcal{A})$ correspond to $R$-good filters. The surprise is
that, unlike the original result by Berkovich, we do not require the field $K$
to be non-trivially valued. Our investigations into non-Archimedean geometry
can be understood as being framed by the question: what is the relationship
between topology and logic?
