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Math Help - Group acting by Isometries

  1. #1
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    Group acting by Isometries

    Hey guys, quick question. What is the definition of a group acting by isometries on a metric space?

    Thanks.
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  2. #2
    MHF Contributor Swlabr's Avatar
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    Re: Group acting by Isometries

    Quote Originally Posted by cavey View Post
    Hey guys, quick question. What is the definition of a group acting by isometries on a metric space?

    Thanks.
    Is it not simply that the group action is an isometry? As in, writing x^g for the action of g on x\in X you have that,

    d(x^g, y^g)=d(x, y).
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  3. #3
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    Re: Group acting by Isometries

    Thanks for the help.
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