Theory of Convergence of Value Sets

Theory of Convergence of Value Sets This work presents a formal mathematical framework titled “SINGEN: Theory of Convergence of Sets of Values”. The paper develops a unified operator-based approach to convergence of sets of values in metric spaces equipped with the Hausdorff distance. The framework is formulated through a contract schema (X, ρ, T, q), where convergence is established under explicitly defined conditions on the operator T. The results are stated in rigorous mathematical form and include formal definitions, theorems, and proofs. The theory provides a structured foundation for analyzing convergence of value sets under deterministic contractive mappings.