Definition:Closure Operator/Notation

Definition
Let $T = \left({S, \tau}\right)$ be a topological space.

Let $H \subseteq S$.

The topological closure of $H$ is variously denoted:
 * $\operatorname{cl} \left({H}\right)$
 * $\operatorname{Cl} \left({H}\right)$
 * $\overline H$
 * $H^-$

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.

$\operatorname{cl} \left({H}\right)$ and $\operatorname{Cl} \left({H}\right)$ are somewhat 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 $\operatorname{cl} \left({H}\right)$ can also be found in places.