Bornological Semigroups with Respect to Semi-Bounded Sets

Abstract

The main goal of this work, is to study new classes of bornological semi group with respect to S-bounded maps, S*-bounded maps and S**-bounded maps. This manuscript would be useful to give the theoritical solution for problems in bounded and limatation by restrict the condition of boundedness. So, the motivation of this work is to require less restrictive condition on the semigroup operations neither of the operation is required to be bounded. The main important results, we prove that every bornological semigroup is an S-bornological semigroup, S*-bornological semigroup and S**-bornological semigroup. Furthermore, the certain condition for any codomain of S*-bornological semigroup to be S*-bornological semigroup was given. In addition, every left (right) translation is S-bornological isomorphism and S*-bornological isomorphism.