DEPENDENCE ON COUNTABLE MANY OF COORDINATES OF SEPARATELY CONTINUOUS FUNCTIONS OF THREE VARIABLES

Abstract

The dependence of continuous mappings on a certain number of coordinates was intensively studied in the works of many mathematicians in the middle of the 20th century. It has become a convenient tool in the study of properties of continuous mappings. The most general results in this direction were obtained in [5], where the necessary and sufficient conditions for the dependence of continuous functions on products from a certain number of coordinates were obtained. Starting with [8] the dependence of separately continuous mappings on a certain number of coordinates became the subject of research at the Chernivtsi University. For functions of two variables the most general results were obtained in [10]. The dependence on a certain number of coordinates of separately continuous functions of three or more variables was studied in [7], where the necessary and sufficient conditions were established only in the case of metrizability of all factors, which leaves a lot of room for further research. We obtain necessary and sufficient conditions of dependence on countable many of coordinates of functions on the product of three spaces each of which is the product of a family of compact Kempisty spaces.