What is the cardinality of the set of all perfect sets in $\mathbb{R}$?
Is it $2^{2^{\mathbb{N}}}$?
It is $c$ that is cardianlity of $R$ as number of open sets in $R $ is this so number of closed sets is also this.
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It is $c$ that is cardianlity of $R$ as number of open sets in $R $ is this so number of closed sets is also this.