Prove that the unit open ball in $\mathbb{R}^2$ cannot be expressed as a countable disjoint union of open rectangles. Open rectangles in $\mathbb{R}^2$ are subsets of the form $(a,b)\times(c,d)$.
Thanks a lot!
Prove that the unit open ball in $\mathbb{R}^2$ cannot be expressed as a countable disjoint union of open rectangles. Open rectangles in $\mathbb{R}^2$ are subsets of the form $(a,b)\times(c,d)$.
Thanks a lot!