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Math Help - Topology question

  1. #1
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    Topology question

    Helo,I need confirmation on this concept:
    Let (M,d) be a metric space and \phi:M\rightarrow N be a bijective map ,then we can make N a metric space isometric to M by defining a metric d_1 by : distance between
    \phi(x) and \phi(y) equals distance between x and y
    d_1(\phi(x),\phi(y))=d(x,y)
    Last edited by Ackbeet; August 3rd 2011 at 06:21 AM.
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  2. #2
    Super Member girdav's Avatar
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    Re: Topology question

    Quote Originally Posted by facenian View Post
    Helo,I need confirmation on this concept:
    Let (M,d) be a metric space and \phi:M\rightarrow N be a bijective map ,then we can make N a metric space isometric to M by defining a metric d_1 by : distance between
    \phi(x) and \phi(y) equals distance between x and y
    d_1(\phi(x),\phi(y))=d(x,y)
    Yes, it's true. You have to show that indeed d_1 is a metric, and by definition of d_1, \phi is an isometric map.
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