Neutrosophic Tri-metric Space and Its Topological Properties

Jamal Oudetallah; Wedad Alharbi; Rehab Alharbi; Ala Amourah; Abdullah Alsoboh; Faisal  Al-Sharqi; Tala Sasa

Authors

Jamal Oudetallah Department of Mathematics, Faculty of Arts and Sciences, University of Petra, 11196, Amman, Jordan;
Wedad Alharbi Department of Mathematics, College of Science, Jazan University, P.O. Box. 114, Jazan 45142, Kingdom of Saudi Arabia;
Rehab Alharbi Department of Mathematics, College of Science, Jazan University, P.O. Box. 114, Jazan 45142, Kingdom of Saudi Arabia;
Ala Amourah Jadara University Research Center, Jadara University, Jordan.
Abdullah Alsoboh College of Applied and Health Sciences, ASharqiyah University, Post Box No. 42, Post Code No. 400, Ibra, Sultanate of Oman;
Faisal Al-Sharqi Department of Mathematics, Faculty of Education for Pure Sciences, University of Anbar, Ramadi, 55431, Iraq;
Tala Sasa Department of Mathematics, Faculty of Science, Applied Science Private University, Amman, Jordan;

Keywords:

Neutrosophic tri-metric spaces Neutrosophic topology r-compactness D-metacompactness Pairwise expandable spaces Neutrosophic xed point theory.

Abstract

We introduce neutrosophic tri-metric spaces as a novel mathematical framework that generalizes
classical metric space theory by incorporating three interrelated distance functions with neutrosophic compo
nents representing truth, indeterminacy, and falsity. Building upon the foundational work in G-metric spaces
and extending recent developments in r-compactness, D-metacompactness, and pairwise expandable spaces, we
establish comprehensive theoretical foundations for these structures. Our investigation presents twelve funda
mental theorems with detailed proofs, exploring neutrosophic r-compactness, neutrosophic D-metacompactness,
and pairwise neutrosophic expandability. We demonstrate that neutrosophic tri-metric spaces provide a nat
ural framework for modeling geometric uncertainty while maintaining rigorous mathematical properties. The
theoretical architecture developed herein o ers innovative perspectives on multi-valued distance measurement
and establishes connections between neutrosophic topology and classical topological concepts. Our results open
new avenues for research in generalized metric theory and uncertainty modeling in topological spaces.

DOI: 10.5281/zenodo.17074265