Is the collection of all disjoint closed sets in $\mathrm{R} $ countable?
2026-04-02 16:55:42.1775148942
Countability of collection of closed sets in $R$
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I'm a bit confused by your question, I'll try to answer to my interpretation of it.
It is true that any collection of open disjoint sets is countable. But it make no sense to consider the set of all closed (or open) disjoint sets (disjoint from what?). It is anyway not true that any collection of disjoint closed sets is countable, since it is enough to consider the collection of singletons, which are closed.