Karlova O. Classification and extension of analogs of continuous maps

The thesis is devoted to the Baire and Lebesgue classifications of maps of one and several variables and to problems of extension of maps from different functional classes. A generalization of the classical Lebesgue-Hausdorff-Banach result is obtained. A characterization of right and left compositors is given. A new concept of almost strongly zero-dimensional space is introduced and a description of such spaces in terms of Baire's and Lebesgue's classes is obtained. We get general theorems on the Baire and Lebesgue classification of vertically almost separately continuous functions. The Kuratowski Extension Theorem is generalized. We generalize the Kuratowski-Sierpinski theorem on the first class functions with a connected graph. New results on a dependence of continuous functions defined on invariant subsets of uncountable products from countably many coordinates is proved. Pointwise limits of finitely determined continuous functions are investigated.