# Mazur–Ulam theorem

(Redirected from Mazur-Ulam theorem)
In mathematics, the Mazur–Ulam theorem states that if ${\displaystyle V}$ and ${\displaystyle W}$ are normed spaces over R and the mapping
${\displaystyle f\colon V\to W}$
is a surjective isometry, then ${\displaystyle f}$ is affine.