In this paper, we introduce topological notions defined by means of β-open sets when these are planted into the framework of Ying’s fuzzifying topological spaces (by Lukasiewicz logic in [0, 1]).We introduce T 0 β -; T 1 β -; T 2 β - (β- Hausdorff)-, T 3 β - (β-regular)- and T 4 β - (β-normal)-separation axioms. Furthermore, the R 0 β - and R 1 β - separation axioms are studied and their relations with the T 1 β - and  T 2 β - separation axioms are introduced. Moreover, we clarify the relations of these axioms with each other as well as the relations with other fuzzifying separation axioms.