Return to Revisions

2 of 2

clarification of the hypotheses

edit approved Jan 20, 2015 at 23:18

Under what conditions $\|x-y\|=n\iff\|f(x)-f(y)\|=n.$ for $n\in\mathbf{N}$ implies isometry?

Let $X, Y$ be normed space and $f:X\to Y$ be a mapping. Assume that for all $n\in\mathbf{N}$, $$\|x-y\|=n\iff\|f(x)-f(y)\|=n.$$ Under what conditions this map will be an isometry? Thanks

norms isometries

asked Jan 19, 2015 at 14:32

user62498