International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/1664 2020 2020 Department of Mathematics, Annamalai University, Annamalai Nagar - 608 002, India P. Surendra Department of Mathematics, Annamalai University, Annamalai Nagar - 608 002, India; Department of Mathematics, M.Kumarasamy College of Engineering, Karur - 639 113, India K. Chitirakala Department of Mathematics, Annamalai University, Annamalai Nagar - 608 002, India; Department of Mathematics, Arignar Anna Government Arts College, Namakkal - 637 002, India A. Vadivel In this paper, neutrosphic hypersoft δ-open sets are introduced by defining the neutrosophic hypersoft regular open sets, pre-open sets, δ-interior and δ-closure. Under the guidance of these definitions, neutrosophic hyper- soft δ semi-open sets and δ pre-open sets are also introduced. Further, we have deduced inuitionistic hypersoft topology and fuzzy hypersoft topology from the neutrosophic hypersoft topology. Moreover, we discuss about the relations between neutrosphic hypersoft δ-open sets, δ semi-open sets, δ pre-open sets, semi-open sets and pre-open sets and their properties with examples. 2023 2023 93 105 10.54216/IJNS.200407 https://www.americaspg.com/articleinfo/21/show/1664