One of the considerable topics in soft setting is study topology which has enticed attention many researchers. To contribute to this scope, we devote work investigate two classes separation axioms with respect distinct ordinary elements through one generalizations called infrasoft topology. We first formulate concepts infra- t <...

In the present paper, we introduce topological notions defined by means of α-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 −, T 1 −, T 2 (αHausdorff)-, T 3 (α-regular)and T 4 (αnormal)-separation axioms. Furthermore, the R 0− and R 1− separation axioms are studied and their relations with the T 1 − ...

ـــــ In [25], we introduce the notion of r-fuzzy neighborhood filters in smooth topological spaces in sense of Gähler [10], and used it to define and study separation axioms , = , , . Here we continue our study of the axioms of separation in smooth topological spaces. Therefore, we introduce the notion of r-fuzzy neighborhood filter at a set. Then by using this notion we define and study separ...