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Closed sets in Cantor Space that are not Clopen

  1. Aug 5, 2011 #1
    Hi,

    Is there a characterization of subsets of the Cantor space C that are closed but not open? As a totally-disconnected set/space, C has a basis of clopen sets; but I'm just curious of what the closed non-open sets are.
     
  2. jcsd
  3. Aug 10, 2011 #2
    I guess the subsets which don't contain a 'part' of C ( i.e. a small copy of C) are among such sets.These include the subsets containing finitely many points; which are closed but not open.
     
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