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<p>of metric spaces.</p>

<p>The concept of quasi-isometry is especially important in <a href="page.php?w=geometric_group_theory">geometric group theory</a>, following the work of <a href="page.php?w=Mikhail_Leonidovich_Gromov">Gromov</a>.</p>

<p><big>Definition</big></p>
<p>Suppose that  is a (not necessarily continuous) function from one metric space  to a second metric space . Then  is called a quasi-isometry from  to  if there exist constants , , and  such that the following two properties both hold:<br/>
#For every two points  and  in , the distance</p><p>
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