On the topological semigroup of equational classes of finite functions under composition

Jorge Almeida (1) , Miguel Couceiro (2, 3) , Tamas Waldhauser (4)

1 UNIVERSIDADE DO PORTO - Departamento de Matemática Pura, Faculdade de Ciências
2 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision
3 ORPAILLEUR - Knowledge representation, reasonning
4 University of Szeged [Szeged]

We consider the set of equational classes of finite functions endowed with the operation of class composition. Thus defined, this set gains a semigroup structure. This paper is a contribution to the under-standing of this semigroup. We present several interesting properties of this semigroup. In particular, we show that it constitutes a topological semigroup that is profinite and we provide a description of its regular elements in the Boolean case.

Domaines: Mathématiques [math]

Jorge Almeida, Miguel Couceiro, Tamas Waldhauser. On the topological semigroup of equational classes of finite functions under composition. Journal of Multiple-Valued Logic and Soft Computing, 2017, 28 (1), pp.5-28. ⟨hal-01090645⟩