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