CARDINALITY-COSMOLOGY DUALITY: A RIGOROUS MATHEMATICAL FRAMEWORK FOR ISOMORPHIC MAPPING BETWEEN INFINITE NUMBER SET HIERARCHIES AND UNIVERSAL TOPOLOGICAL STRUCTURES

This thesis establishes a revolutionary theoretical framework demonstrating rigorous isomorphic correspondences between the hierarchical structure of infinite number sets and the topological architecture of the observable universe. We introduce the Cardinality-Cosmology Duality Principle (CCDP), which posits that the nested infinities of mathematical number systems—specifically ℕ (natural numbers), ℤ (integers), ℚ (rational numbers), ℝ (real numbers), and ℂ (complex numbers)—exhibit structural homomorphisms with successive scales of cosmic organization, from quantum foam to multiverse configurations.