Closure

In topology, the closure of a set  is the intersection of all closed sets containing . Equivalently, the closure of  is the union of  and all limit points of

A closure operator is an abstract (category theory) form of the topological notion of closure which can be applied to any set . It is a function from  to the power set of  satisfying the following conditions:

* (augmentation)
* If  then  (monotonicity)
* (idempotence)

In the category of topological spaces, this operator is isomorphic to the standard topological one.