(untitled) (European Journal of Pure and Applied Mathematics, 2025)
We introduce a novel mathematical framework for analyzing bitopological spaces through bi-metric structures. Our research establishes the theoretical underpinnings of coupled metric spaces configurations that inherently embrace bitopological structures while expanding conventional metric-based frameworks. We demonstrate key mathematical correspondences linking these bi-metric constructs to their generated topologies and furnish diverse contextual implementations. Our investigation examines completeness properties, stability characteristics, and develops systematic product structures within these frameworks. Furthermore, we identify significant relationships with functional-analytical principles, particularly regarding bi-normed spaces and quasimetric frameworks. The mathematical architecture we propose offers innovative perspectives on the interrelationships between metric frameworks and bitopological domains with implications for functional transformation theories, including practical applications in computer networks, image processing, and economic modeling.