aspg-21-2104-1791472166 20261008150926 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2023 22 2 Sudeep Dey Department of Mathematics, Science College, Kokrajhar, Assam, India ; Department of Mathematics, Central Institute of Technology, Kokrajhar, Assam, India Gautam Chandra Ray Department of Mathematics, Central Institute of Technology, Kokrajhar, Assam, India In this article, we first establish a few relationships among neutrosophic interior, neutrosophic closure, neutrosophic pre-open sets, and neutrosophic pre-closed sets in single-valued neutrosophic topological spaces. Thereafter, we defined neutrosophic pre- style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt; font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman"'> style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-bidi-font-family:"Times New Roman";mso-no-proof: yes'>T font-family:"Cambria Math",serif;mso-bidi-font-family:"Times New Roman"; mso-no-proof:yes'>0 space, neutrosophic pre- style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt; font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman"'> style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-bidi-font-family:"Times New Roman";mso-no-proof: yes'>T font-family:"Cambria Math",serif;mso-bidi-font-family:"Times New Roman"; mso-no-proof:yes'>1 space, and neutrosophic pre- style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt; font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman"'> style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-bidi-font-family:"Times New Roman";mso-no-proof: yes'>T font-family:"Cambria Math",serif;mso-bidi-font-family:"Times New Roman"; mso-no-proof:yes'>2 space based on single-valued neutrosophic topological spaces and studied a few properties and relationships among them. We try to establish some relationships between existing neutrosophic separation axioms and newly defined neutrosophic pre-separation axioms. Finally, we study some hereditary properties of pre-separation axioms. Apart from these, we also explore some results implementing neutrosophic pre-open function, neutrosophic pre-continuous function, neutrosophic pre-irresolute function and neutrosophic pre style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt; font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman"'> style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-bidi-font-family:"Times New Roman"'>​ style='font-size:10.0pt;font-family:"Cambria Math",serif;mso-bidi-font-family: "Times New Roman"'>* -function based on our defined definitions. 2023 15 28 2104 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.220202 https://www.americaspg.com/journal/21/article/2104 https://www.americaspg.com/storage/41695569690.pdf