\begin{definition}[Definition:Disconnected (Topology)/Set/Definition 2]
Let $T = \struct {S, \tau}$ be a topological space.
Let $H \subseteq S$ be a non-empty subset of $S$.
$H$ is a '''disconnected set of $T$''' {{iff}} there exist open sets $U$ and $V$ of $T$ such that all of the following hold:
:$H \subseteq U \cup V$
:$H \cap U \cap V = \O$
:$U \cap H \ne \O$
:$V \cap H \ne \O$
\end{definition}