
Diagonals of separately continuous multivalued
mappings (in Ukrainian) 
Author 
V. V. Mykhaylyuk, O. V. Sobchuk, O. G. Fotiy
vmykhaylyuk@ukr.net, ss220367@ukr.net,
ofotiy@ukr.net
×åðí³âåöüêèé íàö³îíàëüíèé óí³âåðñèòåò

Abstract 
We solve the problem on a construction of a separately continuous mapping with the given diagonal, which is the pointwise limit of a
sequence of continuous mappings with values in an equiconnected space. We construct an example of a closedvalued separately continuous
mapping $f\colon [0,1]^2\multimap \mathbb R$ with an everywhere discontinuous diagonal. The example shows that the results on points of joint continuity for compactvalued separately continuous mappings can not be generalized to the case of closedvalued mappings. 
Keywords 
separately continuous mapping; multivalued mapping; diagonal of mapping 
Reference 
1. Baire R. Sur les fonctions de variables re.elles// Ann. Mat. Pura Appl., ser.3. – 1899. – V.3. – P. 1–123.
2. Calbrix J., Troallic J.P. Aplications separement continues// C.R. Acad. Sc. Paris. Sec. A. – 1979. – V.288.
– P. 647–648.
3. Karlova O., Mykhaylyuk V.V., Sobchuk O.V. Diagonals of separately continuous functions and their
analogs// Topology Appl. – 2013. – V.160. – P. 1–8.
4. Maslyuchenko V.K., Mykhaylyuk V.V., Fotiy O.G. The relations between separately and jointly proprities
of multivalued mappings// Mat. Stud. – 2011. – V.35, ¹1. – P. 106–112.
5. Shouchan Hu., Papageorgion N. Handbook of Multivalued Analysis. Theory. DordrechtBostonLondon:
Kluwer Academic Publ. 1997. – 964 p.

Pages 
9398 
Volume 
39 
Issue 
1 
Year 
2013 
Journal 
Matematychni Studii 
Full text of paper 
PDF 
Table of content of issue 
HTML 