REGULARITY AND GREEN'S RELATIONS FOR SEMIGROUPS OF TRANSFORMATIONS THAT PRESERVE AN EQUIVALENCE

ABSTRACT

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).

Key Words:

• Continuous map
• Equivalence
• Semigroup
• Transformation

Mathematics Subject Classification:

• 20M20
• 54H15

ACKNOWLEDGMENT

The author wishes to express his appreciation to the referee for some valuable comments and suggestions that helped to improve the presentation of this paper.