International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/1184 2020 2020 Department of Mathematics, Chandigarh University, Punjab-140413, India. P. Basker Regional Center for the Professions of Education and Training,Casablanca-Settat, Morocco. Broumi Said In this paper, we introduce a new set called Pythagorean neutrosophic beta-open set with this concept, and we introduce interior and closure of Pythagorean neutrosophic beta-open set in a Pythagorean neutrosophic topological spaces by utilizing beta-open set and we introduce the chii, ii, iiibeta-spaces and di, ii, iiibetaspaces from the pair of distinct points and we have derived the necessary and sufficient conditions by utilizing beta-open sets. We also go through some containment relations for interiors and closures of beta-open sets and studied some of their characteristics. 2022 2022 183 191 10.54216/IJNS.180417 https://www.americaspg.com/articleinfo/21/show/1184