$\mathbb{R}^3$ as the union of disjoint circles

Question

In the question 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, Amer. Math. Monthly. 90, 640-641 (1983). ZBL0521.52011. MR0719756.

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

Answer 1

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.