TOPOLOGICAL STRUCTURE AND FIXED POINT THEORY IN NEUTROSOPHIC MR-METRIC SPACES

Abstract

This paper examines the topological and measure-theoretic properties of neutro-sophic MR-metric spaces (NMR-MS). It is shown that every complete NMR-MS inducesa Hausdorff topology that is first countable, separable, and metrizable. In addition, a fixed point theorem for neutrosophic contraction mappings is established, ensuring existence,uniqueness, μ-almost everywhere convergence, measure-theoretic stability, and exponentialconvergence in measure. The results connect neutrosophic set theory with topology andclassical fixed point theory, offering a unified framework for addressing uncertainty and im-precision in analytical structures. Several examples and applications to integral equationsare included to illustrate the theoretical ndings.