A Classification of Regressive Transformation Semigroups on Chains
Patanee Udomkavanich, Phichet Jitjankarn

TL;DR
This paper classifies regressive transformation semigroups on chains, providing conditions for their isomorphism and applying these results to familiar real number subchains.
Contribution
It offers a comprehensive classification of regressive transformation semigroups on chains, including isomorphism conditions and applications to real number subchains.
Findings
Necessary and sufficient conditions for semigroup isomorphism.
Classification of regressive transformation semigroups on real subchains.
Application of isomorphism theorem to familiar chains.
Abstract
For each subchain of a chain , let denote the semigroup under composition of all full regressive transformations, satisfying for all . Necessary and sufficient conditions for and to be isomorphic are given. This isomorphism theorem is applied to classify the semigroup of regressive transformations where are familiar subchains of , the chain of real numbers.
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Taxonomy
Topicssemigroups and automata theory · Mathematical Dynamics and Fractals · Functional Equations Stability Results
