Bornological Soft Sets

Abstract

The concept of bounded set within this set or space is given by many authors. A bornology is defined on soft set to solve the problems of boundedness for the soft set. Also, we construct soft base and soft subbase as a part of fundamental construction for bornological soft sets. Furthermore, It is a natural to study fundamental construction for bornological soft sets, such as soft subspace, product soft bornology and soft bornological isomorphism. Additionally, a family of bornological soft sets can be a partial ordered set by partial ordered relation and we prove that the intersection of bornological soft sets is bornological soft sets but the union of bornological soft sets is not necessary to be bornological soft sets. The left-right translation is soft bornological isomorphism and the product of bornological soft sets are bornological soft sets. Finally, generate soft bornological structure whose elements are soft unbounded sets.

Keywords

• soft set
• bounded set
• bornological set
• bounded map