those of attainability (in abstract control theory) are connected. We exploit this connection here (see Chapter 5). However, basic attention is paid to the problem of the attainability of elements of a topological space under vanishing perturba­ tions of restrictions. The stability property is frequently missing; the world of unstable problems is of interest for us. We construct regularizing proce­ dures. However, in many cases, it is possible to establish a certain property similar to partial stability. We call this property asymptotic nonsensitivity or roughness under the perturbation of some restrictions. The given prop­ erty means the following: in the corresponding problem, it is the same if constraints are weakened in some "directions" or not. On this basis, it is possible to construct a certain classification of constraints, selecting "di­ rections of roughness" and "precision directions".