A function $f:\mathbb R\to\mathbb R$ is called *Świątkowski* if for any connected subset $C\subset \mathbb R$ and points $a,b\in C$ with $f(a)<f(b)$ there exists a continuity point $x\in C\setminus\{a,b\}$ of the function $f$ such that $f(a)<f(x)<f(b)$.



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> **Problem.** Is each Świątkowski function $f:\mathbb R\to\mathbb R$ with closed graph continuous?
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(The problem was written 01.05.2018 by Julia Wódka from Lódz on [page 108](http://www.math.lviv.ua/szkocka/viewpage.php?page=108) of [Volume 1](http://www.math.lviv.ua/szkocka/viewbook.php?vol=1) of the [Lviv Scottish Book](http://www.math.lviv.ua/szkocka)).



Is each Swiatkowski function with closed graph continuous?
In fact, this problem has been answered affirmatively in [this paper](https://arxiv.org/abs/1903.01937) of T.Banakh, M.Filipczak and J.Wodka, and also by MO-user Dap in his comment to [this MO question](https://mathoverflow.net/questions/299467/a-standard-name-for-a-function-satisfying-the-intermediate-value-theorem). 


