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Diagonals of separately continuous multi-valued
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
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| 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 closed-valued 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 compact-valued separately continuous mappings can not be generalized to the case of closed-valued mappings. |
| Keywords |
separately continuous mapping; multi-valued mapping; diagonal of mapping |
| Reference |
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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 multi-valued mappings// Mat. Stud. – 2011. – V.35, ¹1. – P. 106–112.
5. Shouchan Hu., Papageorgion N. Handbook of Multivalued Analysis. Theory. Dordrecht-Boston-London:
Kluwer Academic Publ. 1997. – 964 p.
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| Pages |
93-98 |
| Volume |
39 |
| Issue |
1 |
| Year |
2013 |
Journal |
Matematychni Studii |
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