On studying bi-\(\Gamma\)-algebra and some related concepts

Document Type : Research Paper


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


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.