Neutrosophic λ-Closed Set and Related Mappings in Neutrosophic Topological Spaces

Studying open and closed set variations is crucial in neutrosophic topology, given the growing significance of neutrosophic sets in various applications. This study introduces neutrosophic 𝜆-closed sets, generalizing neutrosophic closed and pre-closed sets within neutrosophic topological spaces. Their fundamental properties are examined alongside comparisons with various existing neutrosophic sets. To illustrate their significance, we define neutrosophic 𝜆-continuous mapping, neutrosophic 𝜆-closed mapping, and neutrosophic 𝜆-𝑇1/2 spaces, exploring their connections with established mappings. Additionally, new concepts such as neutrosophic-𝑤-continuous, neutrosophic-𝑤-closed, neutrosophic-G𝛼-closed, and neutrosophic-𝛼G-closed mappings are proposed to further enrich neutrosophic topological spaces. Several theorems and counterexamples validate these findings and highlight their theoretical significance.