# Category:Definitions/Isometries

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This category contains definitions related to Isometries in the context of Metric Space.

Related results can be found in Category:Isometries.

Let $M_1 = \tuple {A_1, d_1}$ and $M_2 = \tuple {A_2, d_2}$ be metric spaces or pseudometric spaces.

Let $\phi: A_1 \to A_2$ be a bijection such that:

- $\forall a, b \in A_1: \map {d_1} {a, b} = \map {d_2} {\map \phi a, \map \phi b}$

Then $\phi$ is called an **isometry**.

That is, an **isometry** is a distance-preserving bijection.

## Pages in category "Definitions/Isometries"

The following 5 pages are in this category, out of 5 total.