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A classification of regressive transformation semigroups on chains

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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, α:X→X′ satisfying xα≤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 ℝ, the chain of real numbers.

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Acknowledgements

The authors would like to thank the anonymous referees for helpful comments to improve the manuscript. Their constructive and detailed suggestions are very much appreciated.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok, 10330, Thailand

    Patanee Udomkavanich

  2. Division of Mathematics, School of Science, Walailak University, Nakhon Si Thammarat, 80161, Thailand

    Phichet Jitjankarn

Authors
  1. Patanee Udomkavanich
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  2. Phichet Jitjankarn
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Correspondence to Patanee Udomkavanich.

Additional information

Communicated by Jorge Almeida.

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Udomkavanich, P., Jitjankarn, P. A classification of regressive transformation semigroups on chains. Semigroup Forum 85, 559–570 (2012). https://doi.org/10.1007/s00233-012-9438-7

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  • DOI: https://doi.org/10.1007/s00233-012-9438-7

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