# Definition:Kleene Closure

## Definition

Let $S$ be a set.

The Kleene closure of $S$, denoted $S^*$, is the set of all ordered tuples in $S$.

## Also defined as

Sometimes the Kleene closure is considered to be an algebraic structure, endowed with the concatenation operation $*$.

## Also known as

The Kleene closure is also called the Kleene star, reminiscent of its notation.

## Source of Name

This entry was named for Stephen Cole Kleene.