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

Abstract : 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.
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Submitted on : Wednesday, December 3, 2014 - 8:24:28 PM
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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, Old City Publishing, 2017, 28 (1), pp.5-28. ⟨hal-01090645⟩

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