arXiv subjects
Publications and source records attributed to Tomáš Visnyai.
We prove that for any $α\in[0,ω_1)$ there exists a strongly separately continuous function $f:\ell_\infty\to [0,1]$ such that $f$ belongs to the $(α+1)$'th /$(α+2)$'th/ Baire class and does not belong to the $α$'th Baire class if $α$ is finite /infinite/.
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 $1\le α<ω_1$ there exists a strongly separately continuous function which belongs the $(α+1)$'th Baire class and does not belong to the $α$'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.