\begin{definition}[Definition:Connected (Topology)/Set/Definition 3]
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}}:
:the topological subspace $\struct {H, \tau_H}$ of $T$ is a connected topological space.
\end{definition}