Neutrosophic n-metric spaces: generalized fixed point theory and topological properties

Abstract

In this work, we introduce neutrosophic n-metric spaces, a mathematical framework that extends classical metric theory by incorporating n interrelated distance functions with neutrosophic components representing truth, indeterminacy, and falsity. We establish fundamental properties including separation axioms, completeness characterizations, and the induced topology. Our main contributions include generalized fixed point theorems (Banach contraction principle, metric resonance theorem, and multiplicity results) that reveal new phenomena arising from multi-metric interactions. We develop neutrosophic n-r-compactness and n-D-metacompactness theories, demonstrating how covering properties scale with the number of metrics. Additionally, we establish n-fold pairwise expandability in multi-topological settings. The results provide a rigorous framework for modeling multi-scale uncertainty in mathematical and physical systems.