Zariski topology
1. Definition
Let \(A\) be a commutative ring and \(\mathrm{Spec}(A)\) the zariski spectrum. Then the Zariski topology is defined by the closed sets
\begin{align*} \{V(T) \vert T \subseteq A\} \end{align*}see: vanishing set
2. welldefined
2.1. trivial set
follows from
\begin{align*} V(A) =& \{\mathfrak{p} \in \mathrm{Spec}(A) \vert A \subseteq \mathfrak{p} \} \\ =& \emptyset V(\emptyset) =& \mathrm{Spec}(A) \end{align*}