Information on the thesis

In the thesis we explore the relationships between separate and joint ana-
logues of continuity and install decomposition theorems of continuity, quasicon-
tinuity and more. We introduce general classes of A-quasicontinuous mappings
and mappings that are continuous relatively of system of sets covering quasi-
continuous, 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, α-continuity, B-quasicontinuity in terms
of the closure of the image. We give the characterization of joint quasiconti-
nuity, cliquishness and pointwise discontinuity of mappings of two variables,
and we introduce new properties multivalued mappings for receiving the gen-
eral 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, cover-
ing 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.
Keywords: continuity; quasicontinuity; cliquishness; pointwise discontinu-
ity α-continuity; almost continuity; somewhat continuity; almost somewhat
continuity; pseudoquasicontinuity; B-quasicontinuity; continuity to respect of
system; Hahn property; equicliquishness; transition; weakly quasitransition.