A note on finite generated subsemigroups of T(X,Y)
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It is well known that a countable set of transformations on an innite set X is contained in a two-generated subsemigroup of the full transformation semigroup on X. If Y X, then T(X; Y ), the set of all transformations on X with an image in Y , forms a semigroup of transformations with restricted range, as shown in 1975 by Symons . In this paper, we give a sucient and necessary condition for a countable subset of T(X; Y ) to be contained in a three-generated subsemigroup of T(X; Y ).
Document typePeer reviewed
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SourceMathematics for Applications. 2015 vol. 4, č. 1, s. 25-30. ISSN 1805-3629
- 2015/1