Surjective isometry of normed vector spaces
= Surjective isometry of normed vector spaces
A surjective isometry $u:V\to W$ between normed vector spaces preserves every distance:
$$
\|u(v)-u(w)\|=\|v-w\|.
$$
= Surjective isometry of normed vector spaces
A surjective isometry $u:V\to W$ between normed vector spaces preserves every distance:
$$
\|u(v)-u(w)\|=\|v-w\|.
$$