@article{article_524524, title={α-separation axioms based on Lukasiewicz logic}, journal={Hacettepe Journal of Mathematics and Statistics}, volume={43}, pages={259–277}, year={2014}, author={Sayed, O.r.}, keywords={Lukasiewicz logic,semantics,fuzzifying topology,fuzzifying separation axioms,α-separation axioms}, abstract={<div style="text-align: justify;"> <span style="font-size: 0.9em;">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. </span> </div>}, number={2}, publisher={Hacettepe University}