\begin{definition}[Definition:Connected Between Two Points]
Let $T = \struct {S, \tau}$ be a topological space.
Let $a, b \in S$.
$T$ is '''connected between (the) two points $a$ and $b$''' {{iff}} each separation of $T$ includes a single open set $U \in \tau$ which contains both $a$ and $b$.
\end{definition}