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Homework Help: Sequentailly Compact and Connected

  1. Jul 15, 2008 #1
    1. The problem statement, all variables and given/known data

    Which subset of R are both sequentially compact and connected?

    2. Relevant equations

    3. The attempt at a solution
    The connected subsets of R are the empty set, points, and intervals.
    The subsets of R that are compact are closed and bounded.

    Thus, the subsets of R that are both sequentially compact and connected are closed, bounded continuous intervals. Is this correct?
  2. jcsd
  3. Jul 15, 2008 #2


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    I'm convinced. But I don't think you need to say an interval is 'continuous'. If you mean 'without holes' isn't that automatic?
  4. Jul 16, 2008 #3
    Yes, I see what you mean. Thank you.

    Does anyone know how to close or edit the words "SOLVED" in threads?
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