An Introduction to 𝛿-open sets in a Quadripartitioned Neutrosophic Topological Spaces

In this paper, a systematic framework for 𝛿-open sets and their corresponding 𝛿-closed sets is developed within quadripartitioned neutrosophic topological spaces. The study extends classical topological concepts by embedding them into a quadripartitioned neutrosophic structure. The notions of 𝛿-open sets and 𝛿-closed sets are introduced in this context, and their fundamental properties are investigated in detail. Furthermore, a detailed study is carried out on the behavior of interior and closure operators under the 𝛿-based formulation. Several propositions are established and illustrated through suitable examples to support the theoretical development. The results broaden the scope of generalized topology and establish a foundation for future research in quadripartitioned neutrosophic frameworks.