摘要

In this short note, we describe all the elements in the semigroup S (X, Y) = {f is an element of T-X : f(Y) subset of Y} 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].