The Neutrosophization of δ-Separation Axioms

Fuzzy topology has long been celebrated for its ability to address real-world challenges in areas such as information systems and decision making. However, with ongoing technological advancements and the increasing complexity of practical requirements, the focus has gradually shifted toward neutrosophic topology, a broader and more inclusive framework than fuzzy topology. While neutrosophic topology is primarily rooted in neutrosophic open sets, other related families, including neutrosophic pre-open sets, neutrosophic semi-open sets, and neutrosophic beta-open sets, have also proven instrumental in driving progress in this field. This study introduces neutrosophic δ-open sets as a significant enhancement to the current theoretical framework. In addition, we propose a novel category of separation axioms, termed neutrosophic δ-separation axioms, which are derived from the concept of neutrosophic δ-open sets. Moreover, we explore the interplay between these separation properties and their characteristics within subspaces. Our findings confirm that neutrosophic δ-separation axioms are reliably upheld in neutrosophic regular open subspaces.