Some problems in approximation theory

This dissertation consists of three parts. The first part is devoted to the approximation of a fixed element by a fixed approximating set. In the second part we study approximation by finite sets (Chapter I, Secs. 3?6) and by finite-dimensional subspaces (Chapter II, Secs. 7?15). Selected problems with geometric (Secs. 1?3) and variational (Secs. 4?6) content are considered in the third chapter.
The author's summary of dissertation for the degree of Doctor of Physicomathematical Sciences. The dissertation was defended on December 18, 1970, at a session of the Scientific Council of the Mechanics-Mathematics Faculty of Moscow State University. The official opposition was made up of Academician A. N. Kolmogorov, K. I. Babenko, and S. B. Stechkin.