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A NOTE ON NATURALLY ORDERED SEMIGROUPS OF TRANSFORMATIONS WITH INVARIANT SET
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 91 / Issue 2 / April 2015
- Published online by Cambridge University Press:
- 26 November 2014, pp. 264-267
- Print publication:
- April 2015
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- Article
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In this short note, we describe all the elements in the semigroup
which are left compatible with respect to the so-called natural partial order. This result corrects an error in a paper by Sun and Wang [‘Natural partial order in semigroups of transformations with invariant set’, Bull. Aust. Math. Soc.87 (2013), 94–107].
$$\begin{eqnarray}S(X,Y)=\{f\in {\mathcal{T}}_{X}:f(Y)\subseteq Y\}\end{eqnarray}$$
