Retractions in homotopy theory for finite topological semigroups

Abstract

In this paper we study and develop the retracting property in homotopy theory for finite topological semigroups by introducing the notions of $DS-$retract sets and $US-$retract sets. We show that these sets are stronger forms of strong $S-$deformation retract sets. Furthermore, we study the uniqueness of retraction maps and some topological properties for these retract sets.