On bornological semigroups

In this paper we introduce and study the concept of a bornological semigroup. This generalizes the theory of algebraic semigroup from the algebraic setting to the framework of bornological set. Working with bornological set allows to extend the scope of the latter theory considerably. In this paper we develop and introduce the concept of bornological semigroup and fundamental construction in the class of bornological semigroup and study some of their basic proprieties.