Mazur–Ulam theorem
id:
mazur-ulam-theorem-234-3700386
title:
Mazur–Ulam theorem
text:
In mathematics, the Mazur–Ulam theorem states that if V and W are normed spaces over R and the mapping is a surjective isometry, then f is affine. It was proved by Stanisław Mazur and Stanisław Ulam in response to a question raised by Stefan Banach. For strictly convex spaces the result is true, and easy, even for isometries which are not necessarily surjective. In this case, for any u and v in V , and for any t in [ 0 , 1 ] , write and denote the closed ball of radius R around v by B ¯ . Then t
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wiki
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encyclopedia
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original url:
https://en.wikipedia.org/wiki/Mazur%E2%80%93Ulam_theorem
date created:
date modified:
2023-08-12T01:14:46Z
main entity:
{"identifier":"Q1660147","url":"https://www.wikidata.org/entity/Q1660147"}
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