α-separation axioms based on Lukasiewicz logic

Authors : O.r. SAYED

Pages : 259-277

View : 14 | Download : 5

Publication Date : 2014-04-01

Article Type : Research Paper

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 insert ignore into journalissuearticles values(by Lukasiewicz logic in [0, 1]);. We introduce T α 0 −, T α 1 −, T α 2 insert ignore into journalissuearticles values(α- Hausdorff);-, T α 3 insert ignore into journalissuearticles values(α-regular);- and T α 4 insert ignore into journalissuearticles values(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.
Keywords : Lukasiewicz logic, semantics, fuzzifying topology, fuzzifying separation axioms, α separation axioms