\begin{definition}[Definition:Closed Set/Topology/Definition 1]
Let $T = \struct {S, \tau}$ be a topological space.
Let $H \subseteq S$.
'''$H$ is closed (in $T$)''' {{iff}} its complement $S \setminus H$ is '''open in $T$'''. 
That is, $H$ is '''closed''' {{iff}} $\paren {S \setminus H} \in \tau$.
That is, {{iff}} $S \setminus H$ is an element of the topology of $T$.
\end{definition}