On PR-open set in bi-Alexandroff spaces

In this thesis, we investigate and study the concept of bi- A- space. Using the new concept of pr-open sets, we study the operations of bi- A- space and some results of bi- A- space are introduced. Also, the separation axioms related to pre-𝜏0-space and pr- 𝜏1-space of bi- A- space and the relationship between them with some examples and graphs are given. Furthermore, new types of continuous, open, and closed functions in bi- A- spaces are investigated. Finally, the definition of pre*-continuous function and some important theorems about pre-open, pre-closed, pre-interior, pre-close in these spaces are examined.