Kuratowski closure operator

In topology and related branches of mathematics, the Kuratowski closure axioms are a set of axioms that can be used to define a topological structure on a set. They are equivalent to the more commonly used open set definition. They were first introduced by Kazimierz Kuratowski.

A similar set of axioms can be used to define a topological structure using only the dual notion of interior operator.

Let ${\displaystyle X}$ be a set and ${\displaystyle {\mathcal {P}}(X)}$ its power set.
A Kuratowski Closure Operator is an assignment ${\displaystyle \operatorname {cl} :{\mathcal {P}}(X)\to {\mathcal {P}}(X)}$ with the following properties:

...
Wikipedia