1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    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?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Sequentailly Compact and Connected
Loading...