REGULARITY AND GREEN'S RELATIONS FOR SEMIGROUPS OF TRANSFORMATIONS THAT PRESERVE AN EQUIVALENCE
Pei Huisheng · Communications in Algebra · 2005
Let 𝒯 X denote the full transformation semigroup on a set X. For an equivalence E on X, let Then T E (X) is exactly the semigroup of continuous selfmaps of the topological space X for which the collection of all E-classes is a basis. In this paper, we discuss regularity of elements and Green's relations for T E (X).