Category:Definitions/Isometries (Metric Spaces)
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This category contains definitions related to isometries in the context of metric spaces.
Related results can be found in Category:Isometries (Metric Spaces).
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 (Metric Spaces)"
The following 9 pages are in this category, out of 9 total.
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- Definition:Isometric Metric Spaces
- Definition:Isometry (Metric Spaces)
- Definition:Isometry (Metric Spaces)/Also defined as
- Definition:Isometry (Metric Spaces)/Also known as
- Definition:Isometry (Metric Spaces)/Definition 1
- Definition:Isometry (Metric Spaces)/Definition 2
- Definition:Isometry (Metric Spaces)/Into