Galoitica: Journal of Mathematical Structures and Applications GJMSA 2834-5568 10.54216/GJSMA https://www.americaspg.com/journals/show/2019 2022 2022 Umm Al-Qura Univerity, Mekka, Saudi Arabia Khadija Ben Othman University Of Nizwa, Sultanate Of Oman Oliver Von Shtawzen Mutah University, Faculty of Science, Jordan Ahmad Khaldi Cairo University, Department Of Mathematics, Egypt Rozina Ali This paper is dedicated to study the concept of symbolic neutrosophic metric spaces and refined neutrosophic metric spaces (X(I),d) which are generated by classical metrics, where many elementary properties will be discussed in terms of theorems and examples. Also, we study the topological properties of neutrosophic open balls, closed balls, and their topological metric complements, with many related examples that clarify the validity of our work. 2023 2023 36 42 10.54216/GJMSA.070104 https://www.americaspg.com/articleinfo/33/show/2019