In the question [Covering the space by disjoint unit circles](https://mathoverflow.net/questions/162324/covering-the-space-by-disjoint-unit-circles) the following result is attributed to Sierpinski.



> 
> **Theorem.** The Euclidean space $\mathbb{R}^3$ *is* a union of nondegenerate disjoint circles.
> 
> 
> 


But the usual reference on this result is


*Szulkin, Andrzej*, [**$\mathbb{R}^ 3$ is the union of disjoint circles**](http://dx.doi.org/10.2307/2323284), Amer. Math. Monthly. 90, 640-641 (1983). [ZBL0521.52011](https://zbmath.org/?q=an:0521.52011). [MR0719756](https://mathscinet.ams.org/mathscinet-getitem?mr=719756).


What is the correct reference? I failed to find this result among Sierpinski's works.



$\mathbb{R}^3$ as the union of disjoint circles
You seem to be correct. I was wrong, probably because this result appears in Ciesielski's book (*"Set theory for the working mathematician"* CUP, 1997; Theorem 6.1.3) near a result of Sierpinski. I corrected my question accordingly.


