aspg-21-2938-1791475961 20261008161241 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2025 25 1 Raed Hatamleh Department of Mathematics, Faculty of Science and Information Technology, Jadara University, P.O. Box 733, Irbid 21110, Jordan Ayman Hazaymeh Department of Mathematics, Faculty of Science and Information Technology, Jadara University, P.O. Box 733, Irbid 21110, Jordan In this paper, we present the topological space of intervals based neutrosophic real numbers style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font: major-bidi'>a+bI , 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 130 136 2938 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.250111 https://www.americaspg.com/journal/21/article/2938 https://www.americaspg.com/storage/01719703136.pdf