Category:Isometries
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This category contains results about Isometries in the context of Metric Spaces.
Definitions specific to this category can be found in Definitions/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.
Subcategories
This category has the following 7 subcategories, out of 7 total.
Pages in category "Isometries"
The following 20 pages are in this category, out of 20 total.
D
E
I
- Isometric Image of Cauchy Sequence is Cauchy Sequence
- Isometric Metric Spaces are Homeomorphic
- Isometry between Metric Spaces is Continuous
- Isometry between Metric Spaces is Continuous/Corollary
- Isometry is Homeomorphism of Induced Topologies
- Isometry of Metric Spaces is Equivalence Relation
- Isometry of Metric Spaces is Homeomorphism
- Isometry Preserves Sequence Convergence