α-separation axioms based on Lukasiewicz logic

Abstract

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 α 0 −, T α 1 −, T α 2 (α- Hausdorff)-, T α 3 (α-regular)- and T α 4 (αnormal)-separation axioms. Furthermore, the R α 0 − and R α 1 − separation axioms are studied and their relations with the T α 1 − and T α 2 − 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.