Is a set of circles in $\mathbb{R}^2$ such that no two circles (not discs) overlap necessarily countable or possibly uncountable?
2026-03-25 19:04:55.1774465495
Is a set of circles in $\mathbb{R}^2$ such that no two circles (not discs) overlap necessarily countable or possibly uncountable?
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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.