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Could someone specify a metric on (0,1)

  1. Feb 11, 2013 #1
    could someone specify a metric on (0,1) that defines (the same topology) as the abs. value (i.e. usual) metric and makes this open interval into a complete set?

  2. jcsd
  3. Feb 11, 2013 #2
    Re: Homeomorphism

    There is a homeomorphism [itex]T:(0,1)\rightarrow \mathbb{R}[/itex]. Pull back the metric from [itex]\mathbb{R}[/itex]. Thus define

    [tex]d(x,y)= |T(x)-T(y)|[/tex]
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