Suchergebnisse

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.

In this paper, we introduce the notation of the soft bornological group to solve the problem of boundedness for the soft group. We combine soft set theory with bornology space to produce a new structure which is called soft bornological group. So that both the product and inverse maps are soft bounded. As well as, we study the actions of the soft bornological group on the soft bornological sets. The aim soft bornological set is to partition into orbital classes by acting soft bornological group on the soft bornological set. In addition, we explain the centralizer, normalizer, and stabilizer in details. The main important results are to prove that the product of soft bornological groups is soft bornological group and the action for different elements are the same actions.