\begin{definition}[Definition:Principal Open Subset of Spectrum]
Let $A$ be a commutative ring with unity.
Let $f \in A$.
The '''principal open subset''' determined by $f$ of the spectrum $\Spec A$ is the complement of the vanishing set $\map V f$:
:$\map D f = \Spec A - \map V f$
That is, it is the set of prime ideals $\mathfrak p \subseteq A$ with $f \notin \mathfrak p$.
\end{definition}