On metric properties of spaces in classification problems

The algebraic approach to the problem of synthesizing correct classification algorithms is presented. It is assumed that all the problems are subject to a system of universal constraints. Each problem is determined by a pair of matrices that include an information matrix and an informational matrix. For any informational matrix there exists an information matrix such that the problem is unsolvable. The minimum in the diameter of the compact set of information matrices is over all pairs of problems with any common information matrix and different informational matrices. The notions of the diameter of a compact set of information matrices and the quantum of variation of informational matrices can be localized for particular problems. The metric properties of spaces in classification problems are studied in relation to the stability of classification algorithms and their models.