(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Determine whether the following statements are true or false

a) Every pairwise disjoint family of open subsets of ℝ is countable.

b) Every pairwise disjoint family of closed subsets of ℝ is countable.

2. Relevant equations

part (a) is true. we can find 1-1 correspondence with rational numbers

But part (b) I know it is false. I need a counter example. Could you help me with that?

3. The attempt at a solution

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# Uncountable family of disjoint closed sets

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