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Nonsurjective isometry need not preserve midpoints

Surjectivity in the Mazur-Ulam theorem is essential. The map
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preserves all distances and fixes zero, but it is not linear and does not preserve every midpoint.

Ancestors (7)

  1. Surjective isometry of normed vector spaces
  2. Normed vector space
  3. Functional analysis
  4. Analysis
  5. Area of mathematics
  6. Mathematics
  7. Home

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