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arXiv · 1602.00845

Diagonals of separately continuous multi-valued mappings

O. Fotiy·V. Mykhaylyuk·O. Sobchuk
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Abstract

We solve a problem on a construction of a separately continuous mapping with the given diagonal, which is the pointwise limit of a sequence of continuous mappings valued in an equiconnected space. We construct an example of a closed-valued separately continuous mapping $f:[0,1]^2\to \mathbb R$ with an everywhere discontinuous diagonal. The example shows that the results on the joint continuity point set of compact-valued separately continuous mappings can not be generalized to the case of closed-valued mappings.

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O. Fotiy, V. Mykhaylyuk, O. Sobchuk. 2016-02-02. Diagonals of separately continuous multi-valued mappings. https://arxiv.org/abs/1602.00845

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