On core-dominated closed sets in neutrosophic topology

Abstract

Neutrosophic topology has introduced various generalized closed sets to model uncertainty; however, many existing approaches fail to ensure the dominance of true membership over indeterminacy and falsity. To address this limitation, we propose a new class called core-dominated neutrosophic closed sets, which combine a strict dominance condition with structural constraints based on closure and interior operators. We investigate their fundamental properties and relationships with existing closed sets, and introduce the notions of CDN-continuity, CDN-closed maps, and CDN-homeomorphisms. It is shown that these concepts extend classical ones, while the converses do not generally hold, as demonstrated by counterexamples