\begin{definition}[Definition:Perfect Set/Definition 1]
A '''perfect set''' of a topological space $T = \left({S, \tau}\right)$ is a subset $H \subseteq S$ such that:
:$H = H'$
where $H'$ is the derived set of $H$.
That is, where:
:every point of $H$ is a limit point of $H$
and
:every limit point of $H$ is a point of $H$.
\end{definition}