The intersection of $U$ and $V$ is the set $U\cap V$ defined by
\begin{align*} U\cap V & \mathrel {\smash {\overset {\mathclap {\scriptscriptstyle \text{def}}}=}}\bigcap _{z\in \webleft\{ U,V\webright\} }z\\ & \mathrel {\smash {\overset {\mathclap {\scriptscriptstyle \text{def}}}=}}\webleft\{ x\in X\ \middle |\ \text{$x\in U$ or $x\in V$}\webright\} . \end{align*}
