\begin{definition}[Definition:Altered Long Line/Greatest Element]
Let $T = \struct {S, \tau_p}$ denote the '''altered long line''' on the long line $L$.
Let $p$ be the point which is not an element of $L$ upon which the topology $\tau_p$ is generated.
$p$ is the greatest element of $S = L \cup \set p$.
\end{definition}