The story
Named in honor of Stephen Cole Kleene (1909–1994), an American mathematician. The “closure” part comes from the fact that a Kleene closure is closed with respect to concatenation; cf. free monoid.
Etymology from Wiktionary, CC BY-SA 4.0.
Kleene closure
Today it means: The set of all strings of finite length made up of elements of a given set. (Then the Kleene closure is said to be of that given set. For a given set S, its Kleene closure may be denoted as S^*. The Kleene closure includes a string of zero length. Strings are equivalent to ordered tuples but written without the parentheses and commas.) Full definition →