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
„ерн≥вецький нац≥ональний ун≥верситет

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
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Pages 93-98
Volume 39
Issue 1
Year 2013
Journal Matematychni Studii
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