# One more question related to a well known theorem of Sierpinski

For each positive integer n, let E(n) be n-dimensional Euclidean space. An answer to my MATHSTACKEXCHANGE question No. 2191335 informed me that Sierpinski-in an article in Volume 4(1923) of Fundamenta Mathematicae- had constructed an infinite closed and connected subset C of E(3) which is the countable union of (more than one) pairwise disjoint non-empty closed subsets of E(3). Unfortunately, I have not been able to obtain access to this article......My question is: Is there a theorem stating that no infinite closed and connected subset of E(2)-even if unbounded-can be the countable union of (more than one) pairwise disjoint non-empty closed subsets of E(2)?