Nesterenko V. Analogs of continuity: the relationship between separate and joint properties and theorems on decomposition

In the thesis we explore the relationships between separate and joint analogues of continuity and install decomposition theorems of continuity, quasicontinuity and more. We introduce general classes of A-quasicontinuous mappings and mappings that are continuous relatively of system of sets covering quasicontinuous, almost continuous, almost continuous functions, etc., and also we introduce the concept of for transitional maps between arbitrary topological spaces. In particular, we give characterization of almost continuity, bilateral quasicontinuity, somewhat continuity, a-continuity, B-quasicontinuity in terms of the closure of the image. We give the characterization of joint quasicontinuity, cliquishness and pointwise discontinuity of mappings of two variables, and we introduce new properties multivalued mappings for receiving the general theorem of joint continuity. This theorem generalizes a result of A.Buziad and J.-P.Troallic. In addition, through the transition obtained a theorem on the continuity of a finite-dimensional mapping with the closed graph. We introduce the general concept of transition for maps with values in arbitrary topological spaces and we get new theorems on the decomposition of continuity, covering all previous results on the subject. We obtain new theorems about points of continuity and joint quasicontinuity multivalued mappings that generalize relevant results of T.Neubrunn and E. Debs.