### On studying bi-$$\Gamma$$-algebra and some related concepts

Document Type : Research Paper

Authors

1 Ministry of Education, General Directorate of Education in Diyala, Iraq

2 Department of Mathematics and Computer Applications, College of Science, Al-Nahraini University, Baghdad, Iraq

3 Department of Mathematics, College of Computer Science and Mathematics, Tikrit University, Tikrit, Salahaddin, Iraq

Abstract

The aim of this research paper is to introduce the concept of bi-$$\Gamma$$-algebra space (bi-gamma algebra space). The concept of bi-$$\mu$$-measurable set in a bi-$$\Gamma$$-algebra space is defined. With this concept, some properties of bi-$$\Gamma$$-algebra space are proved. We then define various separation axioms for bi-$$\Gamma$$-algebra space such as $$M_{0},M_{1},\ M_{2},\ M_{3},$$ and $$M_{4}$$; then the relationships between them are studied. In addition, the concept of measurable function between two bi-measurable spaces is introduced and some results are discussed.

Keywords