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Definition: Isometry

Let \((X,d_X)\) and \((Y,d_Y)\) be metric spaces and let

\[f:X\mapsto Y\]

be a total map \(f\) is called an isometry, if it preserves the distances, i.e. if

\[d_Y(f(a),f(b))=d_X(a,b)\quad\quad\text{for all }a,b\in X.\]

If such an isometry \(f\) exists, the metric spaces \(X\) and \(Y\) are called isometric.

Table of Contents

1. Proposition: Isometry is Injective

Mentioned in:

Definitions: 1
Proofs: 2
Propositions: 3

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References

Bibliography

1. Knauer Ulrich: "Diskrete Strukturen - kurz gefasst", Spektrum Akademischer Verlag, 2001