?-separation axioms based on Lukasiewicz logic

Abstract

In the present paper, we introduce topological notions defined by meansof ?-open sets when these are planted into the framework of Ying'sfuzzifying topological spaces (by Lukasiewicz logic in [0, 1]). We introduce T?-, T?1-, T?2(?- Hausdorff)-, T?3(?-regular)- and T?(?normal)-separation axioms. Furthermore, the R0- and R?- separation axioms are studied and their relations with the T?1- and T?2-separation axioms are introduced. Moreover, we clarify the relationsof these axioms with each other as well as the relations with otherfuzzifying separation axioms.