# Is each Swiatkowski function with closed graph continuous?

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 $$f(a) there exists a continuity point $$x\in C\setminus\{a,b\}$$ of the function $$f$$ such that $$f(a).

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).