# Definition:Kleene Closure

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## Definition

Let $S$ be a set.

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

The **Kleene closure** is endowed with the concatenation operation $*$:

- $\tuple{ S^*, *}$

to form an algebraic structure.

## 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.

## Also see

## Sources

- 2010: Steve Awodey:
*Category Theory*(2nd ed.) ... (previous) ... (next): $\S 1.7$