ON THE CATEGORIES OF NEUTROSOPHIC SETS AND NEUTROSOPHIC TOPOLOGICAL SPACES

This paper develops a categorical framework for neutrosophic sets and neutrosophic topological spaces. We first redefine the category NSet of neutrosophic sets and investigate its fundamental categorical properties, proving in particular that it is concretely cartesian closed. We also establish relationships among several natural subcategories of NSet. We then introduce the category NTop of neutrosophic topological spaces and prove that it is a topological category. Furthermore, we show that the category of intuitionistic fuzzy topological spaces embeds into NTop, and we identify important subcategories, including CNNTop and the category SNTop of stratified neutrosophic topological spaces, together with their coreflective properties. We identify the Sierpi?ski object in NTop and prove that it serves as the open-set classifier for neutrosophic topological spaces. Finally, we establish that the neutrosophic Sierpi?ski space characterizes NTop as a category of sets with structures and show that the category NTop$_0$ of $T_0$ neutrosophic topological spaces is the epireflective hull of the Sierpi?ski object in NTop.