EDB — 114

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E6

[114]The condition that \(𝜑\) is surjective cannot be removed from the Mazur–Ulam theorem. Find an example.

Hint. By the previous exercise [112], the sphere \(\{ x∈ M_ 2,\| x\| _{M_ 2}=1\} \) must contain segments.

Solution 1

[115]

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  • normed vector space
  • theorem, Mazur–Ulam
  • sphere
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