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Closure and connected spaces

  1. Feb 29, 2012 #1
    If the closure of a space C is connected, is C connected?
  2. jcsd
  3. Feb 29, 2012 #2
    What do you think?? Can you come up with a counterexample?? (this should suggest that the answer is no)
  4. Feb 29, 2012 #3
    What is the usual way to show that the circle is not homeomorphic to the real line?
  5. Feb 29, 2012 #4


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    Can you think of some dense subsets of the real line?
  6. Feb 29, 2012 #5
    There's a really easy counterexample. Just take the real line and ______ one single _______.
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