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Diagonals of separately continuous multi-valued mappings (in Ukrainian)

Keywords: separately continuous mapping , multi-valued mapping , diagonal of mapping

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Abstract:

We solve the problem on a construction of a separatelycontinuous mapping with the given diagonal, which is thepointwise limit of a sequence of continuous mappings withvalues in an equiconnected space. We construct an example of aclosed-valued separately continuous mapping $fcolon[0,1]^2multimap mathbb R$ with an everywhere discontinuousdiagonal. The example shows that the results on points of jointcontinuity for compact-valued separately continuous mappingscan not be generalized to the case of closed-valued mappings.

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