Embedding and Approximation Theories in the Context of Computational (Numerical) Diameter and Internal Problems of the Theory of Functions

The Computational (numerical) diameter, as we see it, is quite distinctly at the level "For all times!" formulates the main tasks of the Approximation Theory, Computational Mathematics and Numerical Analysis with the accompanying computer service maintenance. Moreover, already at the task formulation stage, the corresponding unimprovable theorems of the theory of embeddings are among the first requirements for the correctness of the statement. At the same time, as P.L. Ulyanov claimed, that "internal problems" were in the Embedding Theorems and Approximation Theory. This article is devoted to this.