\begin{definition}[Definition:Connected (Topology)/Topological Space/Definition 1]
Let $T = \struct {S, \tau}$ be a topological space.
$T$ is '''connected''' {{iff}} it admits no separation.
That is, $T$ is '''connected''' {{iff}} there exist no open sets $A, B \in \tau$ such that $A, B \ne \O$, $A \cup B = S$ and $A \cap B = \O$.
\end{definition}