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

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.