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Homework Help: Metric spaces - is my answer right?

  1. Apr 22, 2010 #1
    1. The problem statement, all variables and given/known data
    Give an example of two metric spaces (X1, d1) and (X2, d2) which are topologically equivalent and for which (X1, d1) is complete and (X2, d2) is not.

    2. The attempt at a solution
    The open unit disc and R2. They are homeomorphic, but there are Cauchy sequences in the disc which will converge to limits outside of the disc, so it's not complete.
  2. jcsd
  3. Apr 22, 2010 #2


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    I can't argue with your reasoning.
  4. Apr 22, 2010 #3
    Thanks - I was pretty sure, but wanted to check.
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