  The notion of a labelled space was introduced by Bates and Pask in
generalizing certain classes of C*-algebras. Motivated by Exel's work on
inverse semigroups and combinatorial C*-algebras, we associate each weakly left
resolving labelled space with an inverse semigroup, and characterize the tight
spectrum of the latter in a way that is reminiscent of the description of the
boundary path space of a directed graph.
