Melnyk V. Uniform distances to different functional classes and development of Hahn's theorem on intermediate function

The Dissertation is dedicated to investigation of possibility of transfer of the results of Hahn-Dieudonne-Tong-Katetov theorem on intermediate continuous function for two semicontinuous lower and upper respectively functions for other classes of functions. Also, uniform distances from functions to different classes of functions. We constructed intermediate affine function for convex and concave functions given on vector space. Also we have constructed strictly intermediate differentiable functions for strict Hahn's pairs on segments, parallelepipeds, asplund and Hilbert spaces. With the help of cross topology there were received a number of results on transfer of Hahn's result to the case of separately continuous functions on products of topological spaces, and also for multivalued Hahn's pairs.