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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 $f(a)<f(x)<f(b)$.

Problem. Is each Świątkowski function $f:\mathbb R\to\mathbb R$ with closed graph continuous?

(The problem was written 01.05.2018 by Julia Wódka from Lódz on page 108 of Volume 1 of the Lviv Scottish Book).

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In fact, this problem has been answered affirmatively in this paper of T.Banakh, M.Filipczak and J.Wodka, and also by MO-user Dap in his comment to this MO question.

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