The paper's first part is devoted to the construction of systems, finitary in Rⁿ, of functions[Figure not available: see fulltext.] for approximations of the form The concepts of ℓ-approximating and[Figure not available: see fulltext.]-interpolating systems of functions[Figure not available: see fulltext.] are introduced, methods of constructing them are examined, and the labor consumption of the matrices of a variational-difference method is discussed when different systems of functions[Figure not available: see fulltext.] are used. The paper's second part contains inverse approximation theorems for metric spaces and their application in the case of approximations by spaces of local functions in Sobolev norms.