The choice of correctness classes

We present a general topological approach for analyzing a broad class of inverse problems that arise in processing information flows. These problems often involve the lack of continuity in the inverse operator due to the a priori assignment of topologies in the space of admissible solutions and given data. To address such ill-posed problems, researchers widely use A.N. Tikhonov's regularization method. We propose an approach to identifying correctness classes for inverse problems by aligning the topologies of source data and generalizing the concept of the solution space. This ensures the continuous dependence of the solution on the source data. We also examine correctness classes based on the Zermelo selection principle. The proposed approach can support the development of stable artificial neural networks (ANN) for pattern recognition tasks and may extend to artificial intelligence (AI) system technologies.