International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/2938 2020 2020 Department of Mathematics, Faculty of Science and Information Technology, Jadara University, P.O. Box 733, Irbid 21110, Jordan admin admin Department of Mathematics, Faculty of Science and Information Technology, Jadara University, P.O. Box 733, Irbid 21110, Jordan Ayman Hazaymeh In this paper, we present the topological space of intervals based neutrosophic real numbers , where we clarify how neutrosophic real intervals can be expressed according to the neutrosophic partial order relation, and we use these intervals to build a topological space. On the other hand, we use a similar argument to build a topological space over the intervals of refined neutrosophic numbers, with many illustrated and related examples on open and closed sets.     2025 2025 130 136 10.54216/IJNS.250111 https://www.americaspg.com/articleinfo/21/show/2938