Definition:Isometry (Metric Spaces)

Definition 2
Such metric spaces $M_1$ and $M_2$ are defined as being isometric.

Also defined as
Some sources do not insist that an isometry be surjective.

Make sure to know which prerequisites are used when quoting results about isometries.

Also known as
An isometry is also known as a metric equivalence.

Two isometric spaces can also be referred to as metrically equivalent.

Texts which approach the subject from the direction of applied mathematics and physics refer to such a mapping as a rigid motion.

Also see

 * Equivalence of Definitions of Isometry of Metric Spaces
 * Isometry is Homeomorphism of Induced Topologies
 * Distance-Preserving Surjection is Isometry of Metric Spaces