Free Monoid Theory: Maximality and Completeness in Arbitrary Submonoid
Résumé
In this paper, we discuss the different notions of local topological density for subsets of the free monoid A*. We introduce the notion of weak completeness for a set X, relatively to an arbitrary submonoid M of A*. For the so-called strongly M-thin codes, we estabish that weak completeness is equivalent to maximality in M. This constitutes a new generalization of a famous result due a Schtützenberger.