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Homework Help: Banach Space and Compactness

  1. Dec 4, 2008 #1
    1. The problem statement, all variables and given/known data
    Consider the Banach Space [tex]l^{1}[/tex]. Let S={[tex]x \in l^{1}|\left\|x\right\|<1[/tex]}. Is S a compact subset of [tex]l^{1}[/tex]? prove or Disprove.
     
  2. jcsd
  3. Dec 5, 2008 #2

    morphism

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    S isn't even closed. A more interesting problem is whether the closure of S is compact, and I suspect this is what you're supposed to work on.
     
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