International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/1023 2020 2020 Department of Mathematics, Tripura University, Agartala, 799022, Tripura, India Suman .. Department of Mathematics, Tripura University, Agartala, 799022, Tripura, India Rakhal .. Department of Mathematics, Nandalal Ghosh B.T. College, Panpur, Narayanpur, 743126, West Bengal, India Surapati .. Department of Mathematics, Tripura University, Agartala, 799022, Tripura, India Binod Chandra Tripathy In this article an attempt is made to introduce the notion of neutrosophic infi-topological space as an extension of infi-topological space and fuzzy infi-topological space. Besides, we define some open sets, namely, neutrosophic infi-open set, neutrosophic infi-semi-open set, neutrosophic infi-pre-open set, neutrosophic infi-b-open set. Then, we define some continuous functions namely, neutrosophic infi-continuous function, neutrosophic infi-semi-continuous function, neutrosophic infi-pre-continuous function, neutrosophic infi-b-continuous function via neutrosophic infi-topological space. Further, we formulate several interesting results on them via neutrosophic infi-topological spaces. 2022 2022 199 209 10.54216/IJNS.180204 https://www.americaspg.com/articleinfo/21/show/1023