A classification of regressive transformation semigroups on chains |
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Authors: | Patanee Udomkavanich Phichet Jitjankarn |
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Affiliation: | 1. Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok, 10330, Thailand 2. Division of Mathematics, School of Science, Walailak University, Nakhon Si Thammarat, 80161, Thailand
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Abstract: | For each subchain X?? of a chain X, let T RE (X,X??) denote the semigroup under composition of all full regressive transformations, ??:X??X?? satisfying x????x for all x??X. Necessary and sufficient conditions for T RE (X,X??) and T RE (Y,Y??) to be isomorphic are given. This isomorphism theorem is applied to classify the semigroup of regressive transformations T RE (X,X??) where X is one of several familiar subchains of ?, the chain of real numbers. |
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