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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

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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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I don't understand what is being asked. The first sentence of the article you linked to says that the empty set is unique, and your wording implies that you know that it is a subset of the Cantor set. –  Jonas Meyer Jul 4 '11 at 20:49
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up vote 6 down vote accepted

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.

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