Abstract
Abstract Given a regular language L, we effectively construct a unary semigroup that recognizes the topological closure of L in the free unary semigroup relative to the variety of unary semigroups generated by the pseudovariety 𝖱 {\mathsf{R}} of all finite ℛ {\mathcal{R}} -trivial semigroups. In particular, we obtain a new effective solution of the separation problem of regular languages by 𝖱 {\mathsf{R}} -languages.
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