Is a set of circles in $\mathbb{R}^2$ such that no two circles (not discs) overlap necessarily countable or possibly uncountable?

487 Views Asked by At

Is a set of circles in $\mathbb{R}^2$ such that no two circles (not discs) overlap necessarily countable or possibly uncountable?

1

There are 1 best solutions below

0
On

If you take all the circles with a center $(0,0)$ you have an uncountable set of circles that do not overlap (i.e. have pairwise empty intersection). Thus such a set does not need to be countable.