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Totally bounded sets

  1. Oct 17, 2011 #1
    1. The problem statement, all variables and given/known data
    Show that
    If S is totally bounded in ℂ, then the S closure is also totally bounded in ℂ.

    2. Relevant equations

    3. The attempt at a solution

    Assume S is totally bounded. then for very ε>0 there are finitely many discs (O=Union of finitely many discs) that covers S let x be a limit points of S that is in S closure. but not in S.
    hence x is in O (how can I show this?)
    So x is in O for all x in S closure.
    Hence S closure is totally bounded.

    Am I on the right track?
  2. jcsd
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