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Metric spaces

  1. Mar 14, 2007 #1
    1. The problem statement, all variables and given/known data

    i am required to prove whether the following statement is true or false,

    2. Relevant equations

    there exists a metric space (X,d) with B1 contained in B2 contained in
    X such that B1=Bo(x1,3), B2=Bo(x2,2), and B2-B1 not equal to the empty set

    here Bo denotes the open ball

    3. The attempt at a solution

    any hints on how to set about this problem?
     
  2. jcsd
  3. Mar 14, 2007 #2

    Dick

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    Science Advisor
    Homework Helper

    Ok, so your space has to contain at least 3 points, right? x1, x2 and some x in B2-B1. Can you define a metric on those three points that doesn't break any rules (like triangle inequality) and satisfies all of the relations?
     
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