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On the Topological Semigroup of Equational Classes of Finite Functions Under Composition
Jorge Almeida, Miguel Couceiro and Tamás Waldhauser

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 understanding 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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