Cantor proved in 1883 that closed sets of real numbers have the perfect set property, from which it follows that every uncountable closed set of real numbers has the same cardinality as \(\mathbb{R}\). Thus, the CH holds for closed sets. More than thirty years later, Pavel Aleksandrov extended the result to all Borel sets, and then Mikhail Suslin to all analytic sets. Thus, all analytic sets satisfy the CH. However, the efforts to prove that co-analytic sets satisfy the CH would not succeed, as this is not provable in ZFC.