An Approach to Closure and Kernel Defined through N-points

In this paper, we introduce novel definitions of closure and kernel of a neutrosophic set (abbreviated as N-set) based on the newly formulated concept of a N-point. Building upon these foundational ideas, we develop and analyze the key properties of these new notions, which naturally lead to the construction of two previously unstudied N-topologies. These contributions offer fresh insights into the topological behavior of neutrosophic structures. We believe that the proposed framework not only deepens the theoretical understanding of N-sets but also opens new avenues for their application in various fields involving uncertainty, imprecision, and indeterminacy.