# Closure

### From Conservapedia

In topology, the **closure** of a set *A* is the intersection of all closed sets containing *A*. In metric spaces, this can be also defined as the set of all limit points of the set *A*.

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

- (augmentation)
- If then (monotonicity)
- (idempotence)

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