Definition:Closure Operator/Notation

Definition
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, $H^-$ is notation of choice, although $\map \cl H$ can also be found in places.