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Math Help - special metric

  1. #1
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    special metric

    Hi!
    I have one interesting question. Is it possible to find a special metric that a space R is not complete by this metric? I now that the space R is complete with usual Euclidean metric but I don't now about other metrics in this space.
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  2. #2
    Super Member girdav's Avatar
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    Re: special metric

    Put d(x,y)=|e^x-e^y|. It's a metric on \mathbb R, which is topologically equivalent to the usual metric, but the sequence \{-n\} is a Cauchy sequence which is not convergent.
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