1. Limited time only! Sign up for a free 30min personal 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!

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

    User Avatar
    Science Advisor
    Homework Helper

    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.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook




Loading...