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Countable bounded set

  1. May 8, 2009 #1
    1. The problem statement, all variables and given/known data

    given a set A(subset of R(reals)) is bounded.and for all x belongs to R there exists epsilon(eps) such that {(x-eps,x+eps) intersection A} is countable..to prove A is countable

    2. Relevant equations



    3. The attempt at a solution...bdd set in R is totally bounded...but iam not finding the way how to cover A by epsilon cover(has at most countable elements)
     
  2. jcsd
  3. May 8, 2009 #2

    Dick

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    Take a closed interval C containing A and cover it with open intervals having a countable intersection with A. Now use the compactness of the closed interval C.
     
  4. May 8, 2009 #3
    oooooooooooo gr888888888...thanks
     
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