International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/3299 2020 2020 Department of Mathematics, University of Petra, Amman, 1I196, Jordan Jamal Jamal This paper is dedicated to studying for the first time the building of a topological space based on the intervals defined over 4-refined neutrosophic real numbers and 5-refined neutrosophic real numbers, where we define a special partial order relation on these rings, and we use it to study the structure of the corresponding intervals generated from this relation. Also, we characterize the formula of open sets through these two topological spaces with some illustrated examples. 2025 2025 296 306 10.54216/IJNS.250326 https://www.americaspg.com/articleinfo/21/show/3299