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On the Mazur-Ulam Theorem and the Aleksandrov Problem for Unit Distance Preserving Mappings
Let $X$ and $Y$ be two real normed vector spaces. A mapping $f:X \to Y$ preserves unit distance in both directions iff for all $x,y \in X$ with $||x - y|| = 1$ it follows that $||f(x) - f(y)|| = 1$ and conversely. In this paper we shall study, instead …