Interactive Real Analysis5.3. Connected and Disconnected Sets
Examples 5.3.2(d):
Is the Cantor set connected or disconnected ?
The Cantor set is disconnected. In fact, one of the properties of the Cantor set states that it does not contain any open set. Using that fact one can see that the Cantor set must in fact be totally disconnected, which implies disconnected. Can you provide the details ?
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The Cantor set is disconnected. In fact, one of the properties of the Cantor set states that it does not contain any open set. Using that fact one can see that the Cantor set must in fact be totally disconnected, which implies disconnected. Can you provide the details ?
Back