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.