Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Closed sets in Cantor Space that are not Clopen

  1. Aug 5, 2011 #1

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook