\begin{definition}[Definition:Closed Set/Topology/Definition 2]
Let $T = \left({S, \tau}\right)$ be a topological space.
Let $H \subseteq S$.
'''$H$ is closed (in $T$)''' {{iff}} every limit point of $H$ is also a point of $H$.
That is, by the definition of the derived set:
:'''$H$ is closed (in $T$)''' {{iff}} $H' \subseteq H$
where $H'$ denotes the derived set of $H$.
\end{definition}