# Topological Closure is Closure Operator

## Theorem

The topological closure operator is a closure operator.

## Proof

### Extensive

Follows from Set is Subset of its Topological Closure.

### Increasing

Follows immediately from Topological Closure of Subset is Subset of Topological Closure.

### Idempotent

Follows immediately from Closure of Topological Closure equals Closure.

$\blacksquare$