Foundations of Type-1 Neutrosophic Topological Modules

Hussain Wahish; Adel Al-Odhari; Abdulwahed Mhdi; Basheer Al-refaei; Khaled Alhamadi

Authors

Hussain Wahish Department of Mathematics, Faculty of Education and Science, University of Saba Region, Marib, Yemen;
Adel Al-Odhari Department of Mathematics, Faculty of Education, Humanities and Applied Sciences ( khawlan), and Department of Foundations of Sciences, Faculty of Engineering, Sana’a University. Box:13509, Sana’a, Yemen;
Abdulwahed Mhdi Department of Mathematics, Faculty of Education and Science, University of Saba Region, Marib, Yemen;
Basheer Al-refaei Department of Mathematics, Faculty of Education and Science, University of Saba Region, Marib, Yemen;
Khaled Alhamadi Department of Mathematics, Faculty of Science, University of Aden Yemen;

Keywords:

Type-1 Nutrosophic Sets; Type-1 Nutrosophic Topology; Type-1 Nutrosophic Interior Sets;Type-1 Nutrosophic Closure Sets; Type-1 Nutrosophic Exterior Sets; Type-1 Nutrosophic Boundary Sets; Separation Axioms for Ti[I],i = 0,1,...,4).; Continuity on Type-1 Nutrosophic Topological Spaces

Abstract

This paper develops a topological framework based on type-1 neutrosophic sets, extending the
study of uncertainty beyond classical and intuitionistic fuzzy structures. We investigate fundamental oper
ators—interior, closure, and exterior—on type-1 neutrosophic sets X[I], and establish separation axioms for
type-1 topological spaces Ti[I],i = 0,1,...,4). Furthermore, we analyze continuous and contra type-1 neutro
sophic functions, exploring their structural properties within this framework. By isolating type-1 neutrosophic
sets and formalizing their topological behavior, our results provide new insights into neutrosophic topology and
lay the groundwork for broader applications in mathematical analysis, algebra, and related fields.

DOI 10.5281/zenodo.20610008