Definition:Kleene Closure

Definition

Let $S$ be a set.

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

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

• Definition:Concatenation of Ordered Tuples
• Definition:Free Monoid
• Kleene Closure is Monoid

Sources

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