\begin{definition}[Definition:Connected (Topology)/Set/Definition 1]
Let $T = \struct {S, \tau}$ be a topological space.
Let $H \subseteq S$ be a non-empty subset of $S$.
$H$ is a '''connected set of $T$''' {{iff}} it is not the union of any two non-empty separated sets of $T$.
\end{definition}