Uniformities on free semigroups

Jean-Eric Pin (1) , Pascal Weil (2)

1 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications
2 LaBRI - Laboratoire Bordelais de Recherche en Informatique

It is known that the profinite completions of a free semigroup which are associated with a pseudovariety of semigroups or of ordered semigroups, can be defined by an écart or a quasi-écart. We characterize those quasi-écarts and those quasi-uniformities which arise in this fashion. We also prove an Eilenberg-like one-to-one correspondence between pseudovarieties of ordered semigroups and so-called varieties of quasi-uniformities.

Mots clés: Uniform structure; variety of finite semigroups; free semigroup

Domaines: Autre [cs.OH]; Topologie générale [math.GN]; Théorie des groupes [math.GR]; Mathématique discrète [cs.DM]

Jean-Eric Pin, Pascal Weil. Uniformities on free semigroups. International Journal of Algebra and Computation, 1999, 9, pp.431-453. ⟨hal-00113716⟩