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.

Also see

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