# Closure

From Conservapedia

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.