What question did this study set out to answer?

To develop a formal framework for the convergence of sets of values in metric spaces using a unified operator-based approach.

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February 17, 2026Open Access

SINGEN: Theory of convergence of sets of values

Key Points

To develop a formal framework for the convergence of sets of values in metric spaces using a unified operator-based approach.
Introduces a contract schema (X, ρ, T, q) to describe the convergence process.
Employs the Hausdorff distance to measure convergence in metric spaces.
Formulates definitions, theorems, and proofs to support the theoretical framework.
Presents explicit conditions under which convergence occurs for operator T.
Establishes a rigorous mathematical foundation for analyzing convergence of value sets.
Demonstrates the implications of deterministic contractive mappings on convergence.

Abstract

SINGEN: Theory of Convergence of Sets of Values 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.

SINGEN: Theory of convergence of sets of values

Key Points

Abstract

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