\begin{definition}[Definition:Half-Plane/Open]
Let $\PP$ denote the plane.
Let $\LL$ denote an infinite straight line in $\PP$.
Let $\HH$ be a half-plane whose edge is $\LL$.
$\HH$ is an '''open half-plane''' {{iff}} $\HH$ does not include $\LL$.
\end{definition}