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arXiv · 1512.01757

On strongly separately continuous functions on sequence spaces

Olena Karlova·Tomáš Visnyai
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Abstract

We study strongly separately continuous real-valued function defined on the Banach spaces $\ell_p$. Determining sets for the class of strongly separately continuous functions on $\ell_p$ are characterized. We prove that for every $1\le \alpha<\omega_1$ there exists a strongly separately continuous function which belongs the $(\alpha+1)$'th Baire class and does not belong to the $\alpha$'th Baire class on $\ell_p$. We show that any open set in $\ell_p$ is the set of discontinuities of a strongly separately continuous real-valued function.

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Olena Karlova, Tomáš Visnyai. 2015-12-06. On strongly separately continuous functions on sequence spaces. https://arxiv.org/abs/1512.01757

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