\begin{definition}[Definition:Closure Operator/Notation]
Let $T = \struct {S, \preccurlyeq}$ or $T = \struct {S, \tau}$ be an ordered structure or topological space.
Let $H \subseteq S$.
The closure operator of $H$ is variously denoted:
:$\map \cl H$
:$\map {\mathrm {Cl} } H$
:$\overline H$
:$H^-$
Of these, it can be argued that $\overline H$ has more problems with ambiguity than the others, as it is also frequently used for the set complement.
$\map \cl H$ and $\map {\mathrm {Cl} } H$ are cumbersome, but they have the advantage of being clear.
$H^-$ is neat and compact, but has the disadvantage of being relatively obscure.
On {{ProofWiki}}, $H^-$ is notation of choice, although $\map \cl H$ can also be found in places.
\end{definition}