Does there exist an empty subset of the Cantor set? Or is the empty set, i.e. $\varnothing$, the only empty subset of the Cantor set? http://en.wikipedia.org/wiki/Empty_set
closed as not a real question by Asaf Karagila, t.b., Andres Caicedo, Jonas Meyer, Willie Wong♦ Jul 5 '11 at 12:37
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As the Wikipedia article says, the empty set, $\emptyset$, is unique: there is only one empty set. It's a subset of every set, empty or not, so it's a subset of the Cantor set, and it's the only empty subset of any set.