Math Help - Group acting by Isometries

1. Group acting by Isometries

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

Thanks.

2. Re: Group acting by Isometries

Originally Posted by cavey
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,

$d(x^g, y^g)=d(x, y)$.

3. Re: Group acting by Isometries

Thanks for the help.