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math.MG2002
The Beckman-Quarles theorem for continuous mappings from R^2 to C^2
Apoloniusz Tyszka
Let ϕ((x_1,x_2),(y_1,y_2))=(x_1-y_1)^2+(x_2-y_2)^2. We say that f:R^2 -> C^2 preserves distance d>=0 if for each x,y \in R^2 ϕ(x,y)=d^2 implies ϕ(f(x),f(y))=d^2. We prove that if x…
math.MG2002
The Beckman-Quarles theorem for continuous mappings from R^n to C^n
Apoloniusz Tyszka
Let ϕ((x_1,...,x_n),(y_1,...,y_n))=(x_1-y_1)^2+...+(x_n-y_n)^2. We say that f:R^n -> C^n preserves distance d>=0 if for each x,y \in R^n ϕ(x,y)=d^2 implies ϕ(f(x),f(y))=d^2. We pro…