\begin{definition}[Definition:Closure (Topology)/Metric Space]
Let $M = \struct {A, d}$ be a metric space.
Let $H \subseteq A$.
Let $H'$ be the set of limit points of $H$.
Let $H^i$ be the set of isolated points of $H$.
The '''closure of $H$ (in $M$)''' is the union of all isolated points of $H$ and all limit points of $H$:
:$H^- := H' \cup H^i$
\end{definition}