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Surjective isometry of normed vector spaces

A surjective isometry

u : V \to W

between normed vector spaces preserves every distance:

∥ u (v) - u (w) ∥ = ∥ v - w ∥.

Table of contents 120 3
- Mazur-Ulam theorem Surjective isometry of normed vector spaces 78 1
  - Metric extraction of a midpoint by shrinking diameters Mazur-Ulam theorem 59
- Nonsurjective isometry need not preserve midpoints Surjective isometry of normed vector spaces 29

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